Solve the problem.
-Given a group of students: $\mathrm { G } = \{$ Allen, Brenda, Chad, Dorothy, Eric $\}$, count the number of different ways of choosing a treasurer and a secretary if the two must not be the same sex.
A) 3
B) 10
C) 12
D) 6

Question

Quizplus · Accepted Answer

There are 5 boys and 5 girls. To choose a treasurer and a secretary of different sexes, we can choose a boy as treasurer and a girl as secretary, or a girl as treasurer and a boy as secretary. For the first case, there are 5 ways to choose a boy as treasurer and 5 ways to choose a girl as secretary, so there are 5 * 5 = 25 ways. For the second case, there are 5 ways to choose a girl as treasurer and 5 ways to choose a boy as secretary, so there are 5 * 5 = 25 ways. Therefore, there are a total of 25 + 25 = 50 ways to choose a treasurer and a secretary of different sexes.

Solve the Problem G={\mathrm { G } = \{G={ Allen, Brenda, Chad, Dorothy, Eric

Solve the Problem $\mathrm { G } = \{$ Allen, Brenda, Chad, Dorothy, Eric