Out of 4 girls and 7 boys group, In how many ways can a team of 5 members be selected if the team has no girls?

We are given a group of 4 girls and 7 boys, and we need to select a team of 5 members such that **no girls** are included. In other words, the team must consist of only boys.

Since there are 7 boys in total, and the team must have 5 members, we need to select 5 boys from the 7 boys. The number of ways to choose 5 boys out of 7 is given by the combination formula:

\[
\text{Number of ways} = \binom{7}{5}
\]

The formula for combinations is:

\[
\binom{n}{r} = \frac{n!}{r!(n - r)!}
\]

Now, apply it to our case:

\[
\binom{7}{5} = \frac{7!}{5!(7 - 5)!} = \frac{7!}{5!2!} = \frac{7 \times 6}{2 \times 1} = 21
\]

Thus, the number of ways to select a team of 5 members with no girls is **21**.

---

Would you like more details on this problem or any follow-up questions?

### Related Questions:
1. How many ways can a team be selected if there must be at least 1 girl?
2. How many ways can a team be selected if there are exactly 2 girls?
3. What if the team must include exactly 1 boy and 4 girls?
4. How many ways can we select a team of 5 members if the team must include at least 3 boys?
5. How many different teams can be selected from the entire group of 11 members?

### Tip:
For problems involving selection with restrictions, breaking the group into smaller subgroups (e.g., girls and boys) and handling each separately simplifies the calculation.

Learn how to select a team of 5 members from a group consisting of 7 boys, ensuring that no girls are included. This problem involves combinatorics, specifically using the combination formula C(7, 5), and is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation