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

Answer:

2/7

Step-by-step 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: $\dfrac{2}{7}$

Step-by-step 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 :-

$^3P_1\times ^4C_1=\dfrac{3!}{(3-1)!}\times\dfrac{4!}{(4-1)!}=3\times4=12$

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

$^7P_2=\dfrac{7!}{(7-2)!}=42$

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

$\dfrac{12}{42}=\dfrac{2}{7}$