In how many different ways can a team of 3 boys and 2 girls be formed if there are 4 boys and 5 girls from which to select and robert (one of the boys) must be on the team?

The selection of k object out of n, is done is C(n, k) many ways,

where, 

For example, 

the selection of 2 objects out of 3, can be done in:

many ways.

another example, 

the selection of 2 objects out of 5 can be done in:



many ways.

back to our example, 

there are C(3,2)=3 ways of selecting 2 boys out of 3, to form the 3 boys group together with Robert.

There are C(5,2)=10 many ways to select 2 girls out of 5.

Since any selection of the girls and boys can be combined, we have 3*10=30 different ways of forming the groups.

30