Evaluate the combination:
33C3
Combination Definition:
A unique order or arrangement
Combination Formula:
| nCr = | n! |
| r!(n - r)! |
where n is the number of itemsr is the unique arrangements.
Plug in n = 33 and r = 3
| 33C3 2 | 33! |
| 3!(33 - 3)! |
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 - 3)!
(33 - 3)! = 30!
30! = 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
30! = 265,252,859,812,191,032,188,804,700,045,312
Calculate r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate 33C3
| 33C3 = | 8,683,317,618,811,885,938,715,673,895,318,323,200 |
| 6 x 265,252,859,812,191,032,188,804,700,045,312 |
| 33C3 = | 8,683,317,618,811,885,938,715,673,895,318,323,200 |
| 1,591,517,158,873,146,193,132,828,200,271,872 |
33C3 = 5,456
Excel or Google Sheets formula:
=COMBIN(33,3)
What is the Answer?
33C3 = 5,456
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 = nPrNumber of combination(s) of n items arranged in r unique ways = nCr including subsets of setsThis calculator has 2 inputs.
What 2 formulas are used for the Permutations and Combinations Calculator?
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 matternPr = 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
