Question

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.

Options

• 775

• 776

• 777

• 778

Answer 1

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is 777.

Explanation:

Case I: Team consist 5 batsman, 5 bowlers and 1 wicket-keeper then, number of ways

= ⁶C₅ × ⁷C₅ × ²C₁ = 6 × 21 × 2 = 252

Case II: 4 bowlers, 6 batsman and 1 wicket-keepers

= ⁶C₄ × ⁷C₆ × ²C₁ = 15 × 7 × 2 = 210

Case III: 4 bowlers, 5 batsman and 2 wicket-keepers

= ⁶C₄ × ⁷C₅ × ²C₂ = 15 × 21 × 1 = 315

Total = 252 + 210 + 315 = 777