Question

Q.N0.3

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. give step by step explaination​

Answer 1

14 students: 8M, 6F

a) choice of 14 for a representative

b) %288C1%29%286C1%29 = 48 ways to elect one male and one female

c) Order important: 14P2 = 14*13 = 182 ways of electing P & VP

Answer 2

Answer:

The number  of ways that the class can elect

• 1 class representative=14
• 2 class representatives, 1 male and 1 female=48
• 1 president and 1 vice president=182

Step-by-step explanation:

• Number of male students=8
• Number of female students=6
• Total number of students=8+6=14

Step1: choose 1 representative

• The number of ways to elect 1 representative is given by

        $n=^nC_{r}\\n=^{14}C_{1}\\n=14$

Step2: choose 2 representative

• The number of ways to elect 1 male and 1 female representative is given by

         $n=^nC_{r}\\n=^{8}C_{1}\ ^{6}C_{1}\\n=48$

Step3: choose 1 president and 1 vice president representative

• Number of ways to choose 1 president=14
• number of the ways to choose 1 vice president=13
• total ways to choose both together=182