Question

17. Evaluate. Show your work.

a. 6!

b. 6P5 (little 6, capital p, little 5)


c. 12C3 (little 12, capital C, little 3)

Answer 1

A. The factorial symbol n! indicates the product of all positive integers from 1 to n.

Therefore:

6! = 1 x 2 x 3 x 4 x 5 x 6 = 720

B. The formula for permutation is:

P = n! / (n – r)!

The given value is 6P5 which is the form nPr. Therefore,

P = 6! / (6 – 5)!

P = 720 / 1

P = 720

C. The formula for combination is:

C = n! / r! (n – r)!

The given value is 12C3 which is the form nCr. Therefore,

C = 12! / 3! (12 – 3)!

C = 12! / 3! 9!

Where 12! can be written as 12! = 9! x 10 x 11 x 12

C = 9! (10 x 11 x 12) / 3! 9!

Cancelling 9!:

C = 10 x 11 x 12 / 3!

C = 1,320 / 6

C = 220