Evaluate the combination:
1000C2
Combination Definition:
A unique order or arrangement
Combination Formula:
| nCr = | n! |
| r!(n - r)! |
where n is the number of items
r is the unique arrangements.
Plug in n = 1000 and r = 2
| 1000C2 2 | 1000! |
| 2!(1000 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 1000!
1000! = 1000 x 999 x 998 x 997 x 996 x 995 x 994 x 993 x 992 x 991 x 990 x 989 x 988 x 987 x 986 x 985 x 984 x 983 x 982 x 981 x 980 x 979 x 978 x 977 x 976 x 975 x 974 x 973 x 972 x 971 x 970 x 969 x 968 x 967 x 966 x 965 x 964 x 963 x 962 x 961 x 960 x 959 x 958 x 957 x 956 x 955 x 954 x 953 x 952 x 951 x 950 x 949 x 948 x 947 x 946 x 945 x 944 x 943 x 942 x 941 x 940 x 939 x 938 x 937 x 936 x 935 x 934 x 933 x 932 x 931 x 930 x 929 x 928 x 927 x 926 x 925 x 924 x 923 x 922 x 921 x 920 x 919 x 918 x 917 x 916 x 915 x 914 x 913 x 912 x 911 x 910 x 909 x 908 x 907 x 906 x 905 x 904 x 903 x 902 x 901 x 900 x 899 x 898 x 897 x 896 x 895 x 894 x 893 x 892 x 891 x 890 x 889 x 888 x 887 x 886 x 885 x 884 x 883 x 882 x 881 x 880 x 879 x 878 x 877 x 876 x 875 x 874 x 873 x 872 x 871 x 870 x 869 x 868 x 867 x 866 x 865 x 864 x 863 x 862 x 861 x 860 x 859 x 858 x 857 x 856 x 855 x 854 x 853 x 852 x 851 x 850 x 849 x 848 x 847 x 846 x 845 x 844 x 843 x 842 x 841 x 840 x 839 x 838 x 837 x 836 x 835 x 834 x 833 x 832 x 831 x 830 x 829 x 828 x 827 x 826 x 825 x 824 x 823 x 822 x 821 x 820 x 819 x 818 x 817 x 816 x 815 x 814 x 813 x 812 x 811 x 810 x 809 x 808 x 807 x 806 x 805 x 804 x 803 x 802 x 801 x 800 x 799 x 798 x 797 x 796 x 795 x 794 x 793 x 792 x 791 x 790 x 789 x 788 x 787 x 786 x 785 x 784 x 783 x 782 x 781 x 780 x 779 x 778 x 777 x 776 x 775 x 774 x 773 x 772 x 771 x 770 x 769 x 768 x 767 x 766 x 765 x 764 x 763 x 762 x 761 x 760 x 759 x 758 x 757 x 756 x 755 x 754 x 753 x 752 x 751 x 750 x 749 x 748 x 747 x 746 x 745 x 744 x 743 x 742 x 741 x 740 x 739 x 738 x 737 x 736 x 735 x 734 x 733 x 732 x 731 x 730 x 729 x 728 x 727 x 726 x 725 x 724 x 723 x 722 x 721 x 720 x 719 x 718 x 717 x 716 x 715 x 714 x 713 x 712 x 711 x 710 x 709 x 708 x 707 x 706 x 705 x 704 x 703 x 702 x 701 x 700 x 699 x 698 x 697 x 696 x 695 x 694 x 693 x 692 x 691 x 690 x 689 x 688 x 687 x 686 x 685 x 684 x 683 x 682 x 681 x 680 x 679 x 678 x 677 x 676 x 675 x 674 x 673 x 672 x 671 x 670 x 669 x 668 x 667 x 666 x 665 x 664 x 663 x 662 x 661 x 660 x 659 x 658 x 657 x 656 x 655 x 654 x 653 x 652 x 651 x 650 x 649 x 648 x 647 x 646 x 645 x 644 x 643 x 642 x 641 x 640 x 639 x 638 x 637 x 636 x 635 x 634 x 633 x 632 x 631 x 630 x 629 x 628 x 627 x 626 x 625 x 624 x 623 x 622 x 621 x 620 x 619 x 618 x 617 x 616 x 615 x 614 x 613 x 612 x 611 x 610 x 609 x 608 x 607 x 606 x 605 x 604 x 603 x 602 x 601 x 600 x 599 x 598 x 597 x 596 x 595 x 594 x 593 x 592 x 591 x 590 x 589 x 588 x 587 x 586 x 585 x 584 x 583 x 582 x 581 x 580 x 579 x 578 x 577 x 576 x 575 x 574 x 573 x 572 x 571 x 570 x 569 x 568 x 567 x 566 x 565 x 564 x 563 x 562 x 561 x 560 x 559 x 558 x 557 x 556 x 555 x 554 x 553 x 552 x 551 x 550 x 549 x 548 x 547 x 546 x 545 x 544 x 543 x 542 x 541 x 540 x 539 x 538 x 537 x 536 x 535 x 534 x 533 x 532 x 531 x 530 x 529 x 528 x 527 x 526 x 525 x 524 x 523 x 522 x 521 x 520 x 519 x 518 x 517 x 516 x 515 x 514 x 513 x 512 x 511 x 510 x 509 x 508 x 507 x 506 x 505 x 504 x 503 x 502 x 501 x 500 x 499 x 498 x 497 x 496 x 495 x 494 x 493 x 492 x 491 x 490 x 489 x 488 x 487 x 486 x 485 x 484 x 483 x 482 x 481 x 480 x 479 x 478 x 477 x 476 x 475 x 474 x 473 x 472 x 471 x 470 x 469 x 468 x 467 x 466 x 465 x 464 x 463 x 462 x 461 x 460 x 459 x 458 x 457 x 456 x 455 x 454 x 453 x 452 x 451 x 450 x 449 x 448 x 447 x 446 x 445 x 444 x 443 x 442 x 441 x 440 x 439 x 438 x 437 x 436 x 435 x 434 x 433 x 432 x 431 x 430 x 429 x 428 x 427 x 426 x 425 x 424 x 423 x 422 x 421 x 420 x 419 x 418 x 417 x 416 x 415 x 414 x 413 x 412 x 411 x 410 x 409 x 408 x 407 x 406 x 405 x 404 x 403 x 402 x 401 x 400 x 399 x 398 x 397 x 396 x 395 x 394 x 393 x 392 x 391 x 390 x 389 x 388 x 387 x 386 x 385 x 384 x 383 x 382 x 381 x 380 x 379 x 378 x 377 x 376 x 375 x 374 x 373 x 372 x 371 x 370 x 369 x 368 x 367 x 366 x 365 x 364 x 363 x 362 x 361 x 360 x 359 x 358 x 357 x 356 x 355 x 354 x 353 x 352 x 351 x 350 x 349 x 348 x 347 x 346 x 345 x 344 x 343 x 342 x 341 x 340 x 339 x 338 x 337 x 336 x 335 x 334 x 333 x 332 x 331 x 330 x 329 x 328 x 327 x 326 x 325 x 324 x 323 x 322 x 321 x 320 x 319 x 318 x 317 x 316 x 315 x 314 x 313 x 312 x 311 x 310 x 309 x 308 x 307 x 306 x 305 x 304 x 303 x 302 x 301 x 300 x 299 x 298 x 297 x 296 x 295 x 294 x 293 x 292 x 291 x 290 x 289 x 288 x 287 x 286 x 285 x 284 x 283 x 282 x 281 x 280 x 279 x 278 x 277 x 276 x 275 x 274 x 273 x 272 x 271 x 270 x 269 x 268 x 267 x 266 x 265 x 264 x 263 x 262 x 261 x 260 x 259 x 258 x 257 x 256 x 255 x 254 x 253 x 252 x 251 x 250 x 249 x 248 x 247 x 246 x 245 x 244 x 243 x 242 x 241 x 240 x 239 x 238 x 237 x 236 x 235 x 234 x 233 x 232 x 231 x 230 x 229 x 228 x 227 x 226 x 225 x 224 x 223 x 222 x 221 x 220 x 219 x 218 x 217 x 216 x 215 x 214 x 213 x 212 x 211 x 210 x 209 x 208 x 207 x 206 x 205 x 204 x 203 x 202 x 201 x 200 x 199 x 198 x 197 x 196 x 195 x 194 x 193 x 192 x 191 x 190 x 189 x 188 x 187 x 186 x 185 x 184 x 183 x 182 x 181 x 180 x 179 x 178 x 177 x 176 x 175 x 174 x 173 x 172 x 171 x 170 x 169 x 168 x 167 x 166 x 165 x 164 x 163 x 162 x 161 x 160 x 159 x 158 x 157 x 156 x 155 x 154 x 153 x 152 x 151 x 150 x 149 x 148 x 147 x 146 x 145 x 144 x 143 x 142 x 141 x 140 x 139 x 138 x 137 x 136 x 135 x 134 x 133 x 132 x 131 x 130 x 129 x 128 x 127 x 126 x 125 x 124 x 123 x 122 x 121 x 120 x 119 x 118 x 117 x 116 x 115 x 114 x 113 x 112 x 111 x 110 x 109 x 108 x 107 x 106 x 105 x 104 x 103 x 102 x 101 x 100 x 99 x 98 x 97 x 96 x 95 x 94 x 93 x 92 x 91 x 90 x 89 x 88 x 87 x 86 x 85 x 84 x 83 x 82 x 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
1000! = inf
Calculate (n - r)!:
(n - r)! = (1000 - 2)!
(1000 - 2)! = 998!
998! = 998 x 997 x 996 x 995 x 994 x 993 x 992 x 991 x 990 x 989 x 988 x 987 x 986 x 985 x 984 x 983 x 982 x 981 x 980 x 979 x 978 x 977 x 976 x 975 x 974 x 973 x 972 x 971 x 970 x 969 x 968 x 967 x 966 x 965 x 964 x 963 x 962 x 961 x 960 x 959 x 958 x 957 x 956 x 955 x 954 x 953 x 952 x 951 x 950 x 949 x 948 x 947 x 946 x 945 x 944 x 943 x 942 x 941 x 940 x 939 x 938 x 937 x 936 x 935 x 934 x 933 x 932 x 931 x 930 x 929 x 928 x 927 x 926 x 925 x 924 x 923 x 922 x 921 x 920 x 919 x 918 x 917 x 916 x 915 x 914 x 913 x 912 x 911 x 910 x 909 x 908 x 907 x 906 x 905 x 904 x 903 x 902 x 901 x 900 x 899 x 898 x 897 x 896 x 895 x 894 x 893 x 892 x 891 x 890 x 889 x 888 x 887 x 886 x 885 x 884 x 883 x 882 x 881 x 880 x 879 x 878 x 877 x 876 x 875 x 874 x 873 x 872 x 871 x 870 x 869 x 868 x 867 x 866 x 865 x 864 x 863 x 862 x 861 x 860 x 859 x 858 x 857 x 856 x 855 x 854 x 853 x 852 x 851 x 850 x 849 x 848 x 847 x 846 x 845 x 844 x 843 x 842 x 841 x 840 x 839 x 838 x 837 x 836 x 835 x 834 x 833 x 832 x 831 x 830 x 829 x 828 x 827 x 826 x 825 x 824 x 823 x 822 x 821 x 820 x 819 x 818 x 817 x 816 x 815 x 814 x 813 x 812 x 811 x 810 x 809 x 808 x 807 x 806 x 805 x 804 x 803 x 802 x 801 x 800 x 799 x 798 x 797 x 796 x 795 x 794 x 793 x 792 x 791 x 790 x 789 x 788 x 787 x 786 x 785 x 784 x 783 x 782 x 781 x 780 x 779 x 778 x 777 x 776 x 775 x 774 x 773 x 772 x 771 x 770 x 769 x 768 x 767 x 766 x 765 x 764 x 763 x 762 x 761 x 760 x 759 x 758 x 757 x 756 x 755 x 754 x 753 x 752 x 751 x 750 x 749 x 748 x 747 x 746 x 745 x 744 x 743 x 742 x 741 x 740 x 739 x 738 x 737 x 736 x 735 x 734 x 733 x 732 x 731 x 730 x 729 x 728 x 727 x 726 x 725 x 724 x 723 x 722 x 721 x 720 x 719 x 718 x 717 x 716 x 715 x 714 x 713 x 712 x 711 x 710 x 709 x 708 x 707 x 706 x 705 x 704 x 703 x 702 x 701 x 700 x 699 x 698 x 697 x 696 x 695 x 694 x 693 x 692 x 691 x 690 x 689 x 688 x 687 x 686 x 685 x 684 x 683 x 682 x 681 x 680 x 679 x 678 x 677 x 676 x 675 x 674 x 673 x 672 x 671 x 670 x 669 x 668 x 667 x 666 x 665 x 664 x 663 x 662 x 661 x 660 x 659 x 658 x 657 x 656 x 655 x 654 x 653 x 652 x 651 x 650 x 649 x 648 x 647 x 646 x 645 x 644 x 643 x 642 x 641 x 640 x 639 x 638 x 637 x 636 x 635 x 634 x 633 x 632 x 631 x 630 x 629 x 628 x 627 x 626 x 625 x 624 x 623 x 622 x 621 x 620 x 619 x 618 x 617 x 616 x 615 x 614 x 613 x 612 x 611 x 610 x 609 x 608 x 607 x 606 x 605 x 604 x 603 x 602 x 601 x 600 x 599 x 598 x 597 x 596 x 595 x 594 x 593 x 592 x 591 x 590 x 589 x 588 x 587 x 586 x 585 x 584 x 583 x 582 x 581 x 580 x 579 x 578 x 577 x 576 x 575 x 574 x 573 x 572 x 571 x 570 x 569 x 568 x 567 x 566 x 565 x 564 x 563 x 562 x 561 x 560 x 559 x 558 x 557 x 556 x 555 x 554 x 553 x 552 x 551 x 550 x 549 x 548 x 547 x 546 x 545 x 544 x 543 x 542 x 541 x 540 x 539 x 538 x 537 x 536 x 535 x 534 x 533 x 532 x 531 x 530 x 529 x 528 x 527 x 526 x 525 x 524 x 523 x 522 x 521 x 520 x 519 x 518 x 517 x 516 x 515 x 514 x 513 x 512 x 511 x 510 x 509 x 508 x 507 x 506 x 505 x 504 x 503 x 502 x 501 x 500 x 499 x 498 x 497 x 496 x 495 x 494 x 493 x 492 x 491 x 490 x 489 x 488 x 487 x 486 x 485 x 484 x 483 x 482 x 481 x 480 x 479 x 478 x 477 x 476 x 475 x 474 x 473 x 472 x 471 x 470 x 469 x 468 x 467 x 466 x 465 x 464 x 463 x 462 x 461 x 460 x 459 x 458 x 457 x 456 x 455 x 454 x 453 x 452 x 451 x 450 x 449 x 448 x 447 x 446 x 445 x 444 x 443 x 442 x 441 x 440 x 439 x 438 x 437 x 436 x 435 x 434 x 433 x 432 x 431 x 430 x 429 x 428 x 427 x 426 x 425 x 424 x 423 x 422 x 421 x 420 x 419 x 418 x 417 x 416 x 415 x 414 x 413 x 412 x 411 x 410 x 409 x 408 x 407 x 406 x 405 x 404 x 403 x 402 x 401 x 400 x 399 x 398 x 397 x 396 x 395 x 394 x 393 x 392 x 391 x 390 x 389 x 388 x 387 x 386 x 385 x 384 x 383 x 382 x 381 x 380 x 379 x 378 x 377 x 376 x 375 x 374 x 373 x 372 x 371 x 370 x 369 x 368 x 367 x 366 x 365 x 364 x 363 x 362 x 361 x 360 x 359 x 358 x 357 x 356 x 355 x 354 x 353 x 352 x 351 x 350 x 349 x 348 x 347 x 346 x 345 x 344 x 343 x 342 x 341 x 340 x 339 x 338 x 337 x 336 x 335 x 334 x 333 x 332 x 331 x 330 x 329 x 328 x 327 x 326 x 325 x 324 x 323 x 322 x 321 x 320 x 319 x 318 x 317 x 316 x 315 x 314 x 313 x 312 x 311 x 310 x 309 x 308 x 307 x 306 x 305 x 304 x 303 x 302 x 301 x 300 x 299 x 298 x 297 x 296 x 295 x 294 x 293 x 292 x 291 x 290 x 289 x 288 x 287 x 286 x 285 x 284 x 283 x 282 x 281 x 280 x 279 x 278 x 277 x 276 x 275 x 274 x 273 x 272 x 271 x 270 x 269 x 268 x 267 x 266 x 265 x 264 x 263 x 262 x 261 x 260 x 259 x 258 x 257 x 256 x 255 x 254 x 253 x 252 x 251 x 250 x 249 x 248 x 247 x 246 x 245 x 244 x 243 x 242 x 241 x 240 x 239 x 238 x 237 x 236 x 235 x 234 x 233 x 232 x 231 x 230 x 229 x 228 x 227 x 226 x 225 x 224 x 223 x 222 x 221 x 220 x 219 x 218 x 217 x 216 x 215 x 214 x 213 x 212 x 211 x 210 x 209 x 208 x 207 x 206 x 205 x 204 x 203 x 202 x 201 x 200 x 199 x 198 x 197 x 196 x 195 x 194 x 193 x 192 x 191 x 190 x 189 x 188 x 187 x 186 x 185 x 184 x 183 x 182 x 181 x 180 x 179 x 178 x 177 x 176 x 175 x 174 x 173 x 172 x 171 x 170 x 169 x 168 x 167 x 166 x 165 x 164 x 163 x 162 x 161 x 160 x 159 x 158 x 157 x 156 x 155 x 154 x 153 x 152 x 151 x 150 x 149 x 148 x 147 x 146 x 145 x 144 x 143 x 142 x 141 x 140 x 139 x 138 x 137 x 136 x 135 x 134 x 133 x 132 x 131 x 130 x 129 x 128 x 127 x 126 x 125 x 124 x 123 x 122 x 121 x 120 x 119 x 118 x 117 x 116 x 115 x 114 x 113 x 112 x 111 x 110 x 109 x 108 x 107 x 106 x 105 x 104 x 103 x 102 x 101 x 100 x 99 x 98 x 97 x 96 x 95 x 94 x 93 x 92 x 91 x 90 x 89 x 88 x 87 x 86 x 85 x 84 x 83 x 82 x 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
998! = inf
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 1000C2
| 1000C2 = | inf |
| 2 x inf |
| 1000C2 = | inf |
| inf |
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(1000,2)Common Core State Standards In This Lesson
What is the Answer?
How does the Permutations and Combinations Calculator work?
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r unique ways = nCr including subsets of sets
This calculator has 2 inputs.
What 2 formulas are used for the Permutations and Combinations Calculator?
nCr=n!/r!(n-r)!
What 4 concepts are covered in the Permutations and Combinations Calculator?
- combination
- a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)! - factorial
- The product of an integer and all the integers below it
- permutation
- a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)! - permutations and combinations
