Question

Among the 13 cricket players 4 are bowlers, then how many ways can a cricket team be formed of 11 players in which at least 2 bowlers are included?

Answer 1

The number of ways can be given as follows:

2 bowlers and 9 other players = ⁴C₂ x ⁹C₉

3 bowlers and 8 other players = ⁴C₃ x ⁹C₈

4 bowlers and 7 other players = ⁴C₄ x ⁹C₇

Hence, required number of ways is ⁴C₂ x ⁹C₉ + ⁴C₃ x ⁹C₈ + ⁴C₄ x ⁹C₇

= 6 x 1 + 4 x 9 + 1 x 36 = 78