document.write( "Question 1024550: 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?\r
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Algebra.Com's Answer #639986 by Edwin McCravy(20056) $\"\"$ $\"About$

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

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