Question

how many relay teams of 4 members can be chosen from a 6 member team to run in a relay race?

Answer 1

This is going to be a combination problem not a permutation problem, but it will help to conceptualize this by first selecting one person out of 6. How many ways can you do that?

Answer 2

since only 4 members can be in a team.... 4?

Answer 3

Well, if you have 6 things and you want only one, there are 6 different selections possible. Follow?

Answer 4

yes

Answer 5

If you select out that 1 (in six different ways) you have 5 things from which to select. How many ways can you select 1 thing from 5?

Answer 6

5

Answer 7

Good. So You select 1 thing from 6 for a factor of 6. You select 1 thing form 5, for a factor of 5, etc, until you are done with all 4. So your "intermediate" answer is 6x5x4x3, but you are not done yet. These are groups, oeach of which the order doesn't matter. Still with me?

Answer 8

oh ok. Yes I understand

Answer 9

So, we will have a denominator that will resolve the arbitrary uniqueness we instilled by making them in order. Each group has 4 people. We have to divide by the number of ways we are making the order specified. We have to divide by 4x3x2x1

Answer 10

so divide by 360

Answer 11

4x3x2x1 = 24. Not sure where the 360 came from. So, the numerator is 6x5x4x3 and the denominator is 4x3x2x1. Just simplify.

Answer 12

oh I was doing the numerator. ok, 360/24

Answer 13

thank you

Answer 14

You have it now. Good work!