There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 ar…

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 can be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is:

Answer: 777

Accepted Answer

Possible splits of $(4\text{ or }5\text{ bowlers},\ 5\text{ or }6\text{ batsmen},\ 1\text{ or }2\text{ wicketkeepers})$ summing to 11:

- (4 bowlers, 6 batsmen, 1 wk): $\binom64\binom76\binom21 = 15\times7\times2=210$
- (4 bowlers, 5 batsmen, 2 wk): $\binom64\binom75\binom22 = 15\times21\times1=315$
- (5 bowlers, 5 batsmen, 1 wk): $\binom65\binom75\binom21 = 6\times21\times2=252$

$$\text{Total} = 210+315+252 = 777$$

Solutions · 1