Compute the following:

Question

(1) C(6,3) =

(2) C(7,3) =

(3) C(9,5) =

(4) C(8,2)· C(8,6) =

Answer 1

(1) C(6,3) = 6! /[3! * 3! ]= 6 * 5 * 4 / (3 *2) = 20

(2) C(7,3) = 7! / [4! * 3!] = 7 * 6 * 5 / (3 * 2) = 35

(3) C(9,5) =9! / [4! * 5!] = 9*8*7*6*5/(5*4*3*2) = 126

(4) C(8,2)· C(8,6) = {8!/[6!*2!]} * {8!/[2!*6!]} = {8!/[6!*2!]}^2

=[(8 * 7) / 2]^2 = 28^2 = 784