Question

A cricket team of 11 players is to be selected from 13 players 4 of which are bowlers and 2 wicket keepers. The number of ways to select the team, consisting 1 wicket keeper and at least 3 bowlers is –

• A. 8
• B. 22
• C. 112
• D. None of these

Answer 1

Answer: (B)

22

Answer 2

$\begin{matrix} Bowler(4) & (wk)(2) & rest(7) \\ 3 & 1 & 7 \\ 4 & 1 & 6 \end{matrix}$ = ⁴C₃ × ²C₁ × ⁷ C₇

⁴C₄ × ²C₁ × ⁴C₆ = (4 × 2 × 1) + (1 × 2 × 7)

8 + 14 = 22