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

(One corrrection:(b) three groups consisting of 4, 3, and 3 people, it should be 4,3,3, not 4,3,2)

Solution:

(a)

This is a combination question, we choose 7 from 10 and two groups of 7 and 3 are formed.

C(10,7)=120

So there are 120 ways.

(b)

This is a combination question, we choose 4 from 10, and choose 3 from the remaining 6, three groups of 4, 3 and 3 are formed.

C(10,4)*C(6,3) = 210*20= 4200

So there are 4200 ways to divide three groups of 4,3 and 3.