There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. 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 wicket keeper is

Question

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. 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 wicket keeper is ________.

Smart Achievers · Accepted Answer

(777)

Total number of players = 15

Number of bowlers = 6

Number of batsmen = 7

Number of wicket keepers = 2

$∴$ Total number of ways for which at least 4 bowlers, 5 batsmen and 1 wicket keeper is to be selected

$= {}^{6}C_{4} {}^{7}C_{5} {}^{2}C_{1} + {}^{6}C_{4} {}^{7}C_{6} {}^{2}C_{1} + {}^{6}C_{5} {}^{7}C_{5} {}^{2}C_{1}$

$= 315 + 210 + 252 = 777$

Solution

Q.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. 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 wicket keeper is ________.

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Solution

Q. There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. 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 wicket keeper is ________.

Ans. (777) Total number of players = 15 Number of bowlers = 6 Number of batsmen = 7 Number of wicket keepers = 2 ∴ Total number of ways for which at least 4 bowlers, 5 batsmen and 1 wicket keeper is to be selected =C46 C57 C12+C46 C67 C12+C56 C57 C12 =315+210+252=777

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Q.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. 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 wicket keeper is ________.