From a class of 9 boys and 7 12 students are to be chosen for a competition which includes at least 6 boys and at least 4 . In how many ways can this be done if a particular boys is always chosen?
No. of ways
= 8C5 × 7C6 + 8C6 × 7C5 + 8C7 × 7C4
= 56 × 7 + 28 × 21 + 8 × 35 = 1260
