Evaluate the combination:
24C4
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 = 24 and r = 4
| 24C4 2 | 24! |
| 4!(24 - 4)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 24!
24! = 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
24! = 620,448,401,733,239,409,999,872
Calculate (n - r)!:
(n - r)! = (24 - 4)!
(24 - 4)! = 20!
20! = 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
20! = 2,432,902,008,176,640,000
Calculate r!:
r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24
Calculate 24C4
| 24C4 = | 620,448,401,733,239,409,999,872 |
| 24 x 2,432,902,008,176,640,000 |
| 24C4 = | 620,448,401,733,239,409,999,872 |
| 58,389,648,196,239,360,000 |
Final Answer
24C4 = 10,626
