Question

5 fill in the blank 0 points a club has 25 members, 20 boys and 5 girls. two members are selected at random to serve as president and vice president. what is the probability that both will be girls? write the answer as a fraction in simplest form. type your answer...

Explanation:

Step1: Calculate total permutations

The total number of ways to select 2 members out of 25 for president and vice - president (where order matters) is given by the permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\), here \(n = 25\) and \(r=2\). So \(P(25,2)=\frac{25!}{(25 - 2)!}=\frac{25!}{23!}=25\times24 = 600\).

Step2: Calculate permutations of girls

The number of ways to select 2 girls out of 5 for president and vice - president (order matters) is \(P(5,2)=\frac{5!}{(5 - 2)!}=\frac{5!}{3!}=5\times4=20\).

Step3: Calculate probability

The probability \(P\) that both are girls is the number of favorable outcomes (selecting 2 girls) divided by the number of total outcomes (selecting 2 members from all). So \(P=\frac{20}{600}=\frac{1}{30}\).

Answer:

\(\frac{1}{30}\)