Question

In how many ways can a group of 10 people be divided into:
a. two groups consisting of 7 and 3 people?
b. three groups consisting of 4, 3, and 2 people?

Answer 1

This is a combination

Do you know that 5! = 5x4x3x2x1 =120??

from the 10 people you will choose 7

10! divided by (7!3!)

Once you have your group of 7 then there are only 3 people left to put into the group of 3. That is only 1 way.
I think the answer is 4320 ways.

for 3 groups.

10!/4!6! for the first group

You chose 4 so you have 6 left to choose from.

You have 3 left to choose from

3!/2!1!

You will multiply the values from these 3 combination calculations to get your final answer.

6!/3!3! for the second group.