Question

A community athletic club holds an election to select a president and vice president. The nominations for selection include 4 females and 3 males.

What is the probability that a female is elected president and a male is elected vice president?

Answer 1

2/7

Explanation:

For the president position, there are 4 females from a total of 7 people.

For the vice president position, there are 3 males from 6 people left over.

So the probability is 4/7 × 3/6 = 2/7.

Answer 2

Answer:
`(2)/(7)`

Explanation:

Given : Number of males = 3

Number of females = 4

The number of ways to select a female is elected president and a male is elected vice president :-

`^3P_1* ^4C_1=(3!)/((3-1)!)*(4!)/((4-1)!)=3*4=12`

The total number of ways to select 2 people from 7 :_

`^7P_2=(7!)/((7-2)!)=42`

Now, the probability that a female is elected president and a male is elected vice president will be :-

`(12)/(42)=(2)/(7)`