Techniques of Counting A history class contains 8 male stude

Techniques of Counting A history class contains 8 male students and 6 female students. Find the number n of ways that the class can elect: (a) 1 class representative; (b) 2 class representatives, 1 male and 1 female; (c) 1 president and 1 vice-president.

Solution

Male = 8, Female = 6

a) 1 Class Representative = 14 Ways
b) 2 Class Representative, 1 Male, 1 Female = 8 C 1 * 6 C 1 = 8 * 6 = 48 Ways
c) 1 President and 1 Vice President = 8 C 2 = 8 * 7 / 2 * 1 = 28 Ways