Question

In how many ways can 10 people be divided into three groups with 2, 3, and 5 people respectively?

Answer 1

2100

Explanation:

In how many ways can a group of 10 people be divided into three groups consisting of 2,3, and 5 people?

First, you need to choose 4 people to fill the first group.

The number of ways is (104) which equals to 210.

Then, pick 3 more people out of the remaining 6 to be in the second group. And then, pick 3 more out of the remaining 3.

However, we need to divide it by 2, since we don’t really care on the order of selection of group.

(63)(33)/2=10

So, there are 210 x 10 = 2100 ways

Answer 2

hmmm I read JeremyBrooks answer... I think that it might be different...

i think it is 2520

of the 10 you first choose 2

10 choose 2 = 45 ways

in each of the 45 "chooses" you now

pick a group of 3 of the 8 left

8 choose 3 = that is 56

of the five people left you choose 5

5 choose 5 = 1

so the possibilities are 45*56 * 1 = 2520

Explanation: