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Let's break down the problem step by step:

You are given that the number of ways to select 3 boys from a group of 10 students (boys + girls) is 35. We are tasked with finding how many girls are in the group.

### Let the number of boys be \( x \), and the number of girls will then be \( 10 - x \) (since the total number of students is 10).

The number of ways to choose 3 boys from \( x \) boys is represented by the combination formula:
\[
\binom{x}{3} = 35
\]

This means that:
\[
\frac{x(x-1)(x-2)}{3!} = 35
\]
\[
\frac{x(x-1)(x-2)}{6} = 35
\]
Multiplying both sides by 6:
\[
x(x-1)(x-2) = 210
\]
Now, let's solve this cubic equation:
\[
x(x-1)(x-2) = 210
\]

We'll test small integer values of \( x \):

- For \( x = 7 \):
  \[
  7(7-1)(7-2) = 7 \times 6 \times 5 = 210
  \]

So, \( x = 7 \). This means there are 7 boys.

Thus, the number of girls is:
\[
10 - 7 = 3
\]

### Answer: There are **3 girls** in the group.

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Would you like further details on this solution or have any additional questions?

Here are some related questions you could explore:
1. How does the combination formula work for larger groups?
2. What is the difference between permutations and combinations?
3. How many ways can we choose 2 boys and 1 girl from this group?
4. If the number of girls changes, how does it affect the number of combinations?
5. How can we calculate the probability of selecting a girl from the group?

**Tip:** Always use combinations for selecting items when the order of selection does not matter.

no of ways of selecting 3 boys out of a group 10 students (girls + boys) is equal to 35, find number of girls in the group?

Solve a problem where the number of ways to select 3 boys from a group of 10 students (girls + boys) equals 35. This solution uses the combination formula to calculate the number of boys and, subsequently, the number of girls in the group. Suitable for students in Grades 9-10.

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