A committee of 4 people is chosen from 8 women and 8 men. How many different committees are possible that consist of 2 women and 2 men?


To determine how many different committees are possible that consist of 2 women and 2 men, we need to consider the number of ways to select 2 women from 8 and the number of ways to select 2 men from 8. We can then multiply these two numbers together to find the total number of possible committees.

### Step 1: Choose 2 women from 8

The number of ways to choose 2 women from 8 can be calculated using the combination formula \( \binom{n}{k} \), which represents the number of ways to choose \( k \) items from \( n \) items without regard to the order.

\[
\text{Number of ways to choose 2 women} = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28
\]

### Step 2: Choose 2 men from 8

Similarly, the number of ways to choose 2 men from 8 is:

\[
\text{Number of ways to choose 2 men} = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28
\]

### Step 3: Calculate the total number of committees

Since the selections of women and men are independent, we multiply the number of ways to choose the women by the number of ways to choose the men:

\[
\text{Total number of committees} = 28 \times 28 = 784
\]

So, there are **784** different possible committees that consist of 2 women and 2 men.

---

Would you like more details on any part of this explanation, or do you have any questions?

Here are five related questions:

1. How many different committees are possible if the committee must consist of 3 women and 1 man?
2. What if the committee must consist of 1 woman and 3 men?
3. How many different committees are possible if the committee can be any combination of men and women?
4. What is the probability of randomly selecting a committee that consists of 2 women and 2 men?
5. How does the number of possible committees change if one of the women must always be on the committee?

**Tip:** When dealing with combination problems, always check if the order of selection matters. If it doesn't, use combinations instead of permutations.

Learn how to determine the number of different committees possible by choosing 2 women and 2 men from 8 each. This problem involves combinatorial counting using binomial coefficients and is suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation