Explanation:

Sure, let’s break this down step by step:

- We have 6 girls and 4 boys—so 10 kids total.

- Selecting 4 kids with at least one girl. That means out of the 4 selections, we can’t have zero girls.

- First, let’s figure out total ways to select 4 from 10:

\(\binom{10}{4} = 210\)

- Out of these, how many groups have no girls? That’s just 4 boys, so:

\(\binom{4}{4} = 1\)

- So, groups with at least one girl = total - all boys

\(210 - 1 = 209\)

Let’s connect this to your options:

- Option 1: 214 (Too high)

- Option 2: 206 (Too low)

- Option 3: 210 (That’s total, not at least one girl)

- Option 4: 209 (This is right)

209 is the correct answer. Here's why: it’s all combinations minus the only case where there’s not a single girl in the team. That’s the only way to make sure you never get a group without a girl.