Evaluate the combination:
33C5
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 = 33 and r = 5
| 33C5 2 | 33! |
| 5!(33 - 5)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 33!
33! = 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
33! = 8,683,317,618,811,885,938,715,673,895,318,323,200
Calculate (n - r)!:
(n - r)! = (33 - 5)!
(33 - 5)! = 28!
28! = 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
28! = 304,888,344,611,713,836,734,530,715,648
Calculate r!:
r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate 33C5
| 33C5 = | 8,683,317,618,811,885,938,715,673,895,318,323,200 |
| 120 x 304,888,344,611,713,836,734,530,715,648 |
| 33C5 = | 8,683,317,618,811,885,938,715,673,895,318,323,200 |
| 36,586,601,353,405,662,096,993,546,141,696 |
33C5 = 237,336
You have 1 free calculations remaining
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(33,5)
What is the Answer?
33C5 = 237,336
How does the Permutations and Combinations Calculator work?
Free Permutations and Combinations Calculator - Calculates the following:
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?
nPr=n!/r!nCr=n!/r!(n-r)!
For more math formulas, check out our Formula Dossier
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
