Evaluate the combination:
50C4
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 = 50 and r = 4
| 50C4 2 | 50! |
| 4!(50 - 4)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 50!
50! = 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
50! = 30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984
Calculate (n - r)!:
(n - r)! = (50 - 4)!
(50 - 4)! = 46!
46! = 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
46! = 5,502,622,159,812,088,456,668,950,435,842,974,564,586,819,473,162,983,440,384
Calculate r!:
r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24
Calculate 50C4
| 50C4 = | 30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984 |
| 24 x 5,502,622,159,812,088,456,668,950,435,842,974,564,586,819,473,162,983,440,384 |
| 50C4 = | 30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984 |
| 132,062,931,835,490,128,535,241,110,092,887,174,934,013,235,518,001,979,064,320 |
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(50,4)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
