a cricket team of first 11 players out of 16 including 4 bowlers
and 2 wicket-keepers.in how many ways you can do it so that the
team contain at least 3 bowlers and 1 wicket-keeper?
Do you mean:
1. "the team contain at least 3 bowlers and AT LEAST 1
wicket-keeper"?
or do you mean:
2. "the team contain at least 3 bowlers and EXACTLY 1
wicket-keeper"?
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I'll do them both.
There are:
4 bowlers
2 wicket-keepers
10 non-bowlers-not-wicket keepers.
Case A. There are exactly 3 bowlers, exactly 1 wicket
keeper, and 7 non-bowlers-non-wicket-keepers.
(4C3)(2C1)(10C7) = 960
Case B. There are exactly 3 bowlers, exactly 2 wicket
keepers, and 6 non-bowler-non-wicket-keepers.
(4C3)(2C2)(10C6) = 840
Case C. There are exactly 4 bowlers, exactly 1 wicket
keepers, and 6 non-bowler-non-wicket-keepers.
(4C4)(2C1)(10C6) = 420
Case D. There are exactly 4 bowlers, exactly 2 wicket
keepers, and 5 non-bowler-non-wicket-keepers.
(4C4)(2C2)(10C5) = 252
Answer: 960+840+420+252 = 2472, that's choice (a).
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Considering it to be the other way where there is
exactly 1 wicket-keeper, we omit cases B and D.
Answer: 960+420 = 1380, that's not a choice so it
must have meant AT LEAST 1 wicket-keepers.
Edwin
