Question

You are a gym teacher that needs to make 6 groups. Each group must have 4 students in which only 4 groups would participate in each game. What is the total possible number of combinations?

Answer 1

The total possible number of combinations for the gym teacher to make 4 groups out of 6, where each group contains 4 students, is 15.

Step-by-step explanation:

The question asks for the total possible number of combinations of groups in a scenario where a gym teacher is making 6 groups, with 4 students in each, but only 4 groups will participate in each game. To find the total number of combinations, we use the combinatorics formula for combinations, which is expressed as nCr, where n is the total number of items, and r is the number of items to choose.

In this case, we have a total of 6 groups and we want to choose 4 of them to participate in a game. Therefore, we can calculate the number of combinations as 6C4. Using the formula for combinations, that is the factorial of n divided by the factorial of r multiplied by the factorial of n-r, we get:

• 6! / (4! * (6-4)!) = 720 / (24 * 2) = 720 / 48 = 15 combinations.

Therefore, there are 15 different combinations of groups that the teacher can make to participate in each game.