the math club needs to choose four people for a committee to represent it at the school board meeting. the…

Explanation:

Step1: Identify counting - method

We use combinations since we are choosing a group of people (order does not matter). The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen.

Step2: Calculate total number of possible outcomes

The total number of members $n = 14$ and we want to choose $r = 4$ people for the committee. So, $C(14,4)=\frac{14!}{4!(14 - 4)!}=\frac{14!}{4!×10!}=\frac{14\times13\times12\times11}{4\times3\times2\times1}=1001$.

Step3: Calculate number of favorable outcomes

We want 2 girls out of 9 and 2 boys out of 5. The number of ways to choose 2 girls out of 9 is $C(9,2)=\frac{9!}{2!(9 - 2)!}=\frac{9\times8}{2\times1}=36$. The number of ways to choose 2 boys out of 5 is $C(5,2)=\frac{5!}{2!(5 - 2)!}=\frac{5\times4}{2\times1}=10$. The number of favorable outcomes is the product of these two combinations, so $C(9,2)\times C(5,2)=36\times10 = 360$.

Step4: Calculate probability

The probability $P$ that two girls and two boys are on the committee is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}=\frac{360}{1001}\approx0.36$.

Answer:

The counting - method is combinations. The total number of possible outcomes is 1001. The probability that two girls and two boys are on the committee is approximately 0.36.