Evaluate the following permutation
12P5
Permutation Definition:
An order or arrangement
Permutation Formula:
| nPr = | n! |
| (n - r)! |
where n is the number of items
r is the number of arrangements.
Plug in n = 12 and r = 5
| 12P5 2 | 12! |
| (12 - 5)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate n!:
n! = 12!
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
12! = 479,001,600
Calculate (n - r)!:
(n - r)! = (12 - 5)!
(12 - 5)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate 12P5:
| 12P5 = | 479,001,600 |
| 5,040 |
12P5 = 95,040
Excel or Google Sheets formula:
Excel or Google Sheets formula:=PERMUT(12,5)Common Core State Standards In This Lesson
HSS.CP.B.9
What is the Answer?
12P5 = 95,040
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
