17. Evaluate. Show your work.

a. 6!

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

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

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