Question

A teacher has brought treats for her 10 students. She will give out 3 fruit snacks, 2 teddy grahams, and 5 granola bars. How many ways can she do this.

Answer 1

2520 ways

Explanation:

We can solve this problem with 3 combinations:

First the teacher needs to give 3 fruit snacks to 10 students, so we have a combination of 10 choose 3: C(10,3) = 10! / (3! * 7!) = 120

Then, she needs to give 2 teddy grahams to 7 students (3 already got a snack), so a combination of 7 choose 2: C(7,2) = 7! / (2! * 5!) = 21

The, she gives the 5 granola bars to the other 5 students, so a combination of 5 choose 5: C(5,5) = 1.

Now we just need to multiply the combinations to find the result:

C(10,3) * C(7,2) * C(5,5) = 120 * 21 * 1 = 2520 ways