Answer
↓Steps Explained:↓
Evaluate the combination:
52C5
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 = 52 and r = 5
| 52C5 2 | 52! |
| 5!(52 - 5)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 52!
52! = 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
52! = 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464
Calculate (n - r)!:
(n - r)! = (52 - 5)!
(52 - 5)! = 47!
47! = 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
47! = 258,623,241,511,168,177,673,491,006,652,997,026,552,325,199,826,237,836,492,800
Calculate r!:
r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate 52C5
| 52C5 = | 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464 |
| 120 x 258,623,241,511,168,177,673,491,006,652,997,026,552,325,199,826,237,836,492,800 |
| 52C5 = | 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464 |
| 31,034,788,981,340,182,748,066,613,504,319,524,244,564,993,428,643,676,761,882,624 |
Final Answer
52C5 = 2,598,960Take the Quiz
Related Calculators: Factorials | Multiplication Property Of Inequality | Multiplication Array