committee of politicans

[gmatv09]

A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In how many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?

Please help

[mp2437]

I am getting an answer of 73080.

Total possibilites are:

5C1 * 10C3 * 8C3 + 5C1 * 10C4 * 8C2 + 5C1 * 10C5 * 8C1,
which equals 33600 + 29400 + 10080 = 73080.

[gmatv09]

that is correct ans.

thanks ...