Evaluate the combination:
20C3
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 = 20 and r = 3
| 20C3 2 | 20! |
| 3!(20 - 3)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 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 (n - r)!:
(n - r)! = (20 - 3)!
(20 - 3)! = 17!
17! = 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
17! = 355,687,428,096,000
Calculate r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6
Calculate 20C3
| 20C3 = | 2,432,902,008,176,640,000 |
| 6 x 355,687,428,096,000 |
| 20C3 = | 2,432,902,008,176,640,000 |
| 2,134,124,568,576,000 |
20C3 = 1,140
Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(20,3)Common Core State Standards In This Lesson
HSS.CP.B.9
What is the Answer?
20C3 = 1,140
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.
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)!
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
