Question

A piano teacher is planning to take 4 of her 12 students to a concert. She wants to take 2 girls and 2 boys. How many different arrangements are there if she has 8 girl students and 4 boy students? Be sure to show all of your work.​

Answer 1

Explanation:

To find the number of different arrangements, we can use combinations.

The number of ways to choose 2 girls out of 8 is C(8,2) = 28.

The number of ways to choose 2 boys out of 4 is C(4,2) = 6.

So, the total number of ways to choose 2 girls and 2 boys from 8 girls and 4 boys is:

C(8,2) * C(4,2) = 28 * 6 = 168

Therefore, there are 168 different arrangements for the piano teacher to take 4 of her 12 students to the concert.

Answer 2

To solve the problem, we need to determine the number of ways to choose 2 girls out of 8 and 2 boys out of 4, and then multiply those numbers together to get the total number of arrangements.

The number of ways to choose 2 girls out of 8 is given by the combination formula:

C(8,2) = 8! / (2! * 6!) = 28

Similarly, the number of ways to choose 2 boys out of 4 is:

C(4,2) = 4! / (2! * 2!) = 6

Therefore, the total number of different arrangements of 2 girls and 2 boys that can be chosen from the 12 students is:

28 x 6 = 168

So there are 168 different arrangements possible.

Explanation: