Question

A cricket team of 11 players is to be formed from 20 players including 6 bowlers and 3 wicket keepers. The number of ways in which a team can be formed having exactly 4 bowlers and 2 wicket keepers is

• A. 20790
• B. 6930
• C. 10790
• D. 360

Answer 1

Answer: (A)

20790

Answer 2

The correct option is (A): 20790
Explanation: There are 6 bowlers, 3 wicket keepers and 11 batsman in all. The number of ways in which a team of 4 bowlers, 2 wicket keepers and 5 batsman can be chosen
=$C_4^6\times C_2^3\times C\binom{11}{5}$

=$\frac{6\times5}{2\times1}\times\frac{3\times2}{2\times1}\times\frac{11\times10\times9\times8\times7}{5\times4\times3\times2\times1}$

$=15 × 3 × 462 = 20790$