A cricket team of 11 players is to be chosen from 16 players which includes 5 bowlers and 2 wicket keepers. How many ways can a team be selected if each team must have 3 bowlers and 1 wicket keeper?? Plzzz answer!!

we are to choose 11 players , including at least 3 bowlers and 1 wicket keeper.
out of 16 players , number of bowlers = 5 and the number of wicket keepers = 2
others = 16-(5+2)=9
now the required selection can be done in following manner:
3 B +1W+7Ot(i) case  or 3B+2W+6Ot(ii) case  or 4B+1W+6Ot(iii) case or 4B+2W+5Ot(iv) case or 5B+1W+5Ot(v) case  or 5B+2W+4Ot(vi) case
=C35.C12.C79+   C35.C22.C69+  C45.C12.C69+       C45.C22.C59+  C55.C12.C59 +  C55.C22.C49=10*2*36 +10*1*84 + 5*2*84 + 5*1*126 +1*2*126 +1*1*126=720+840+840+8*126=2400+1008=3408

hope this helps you

  • -21

16C3 * 13C1 * 12C7

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