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A cricket team consist of 11 players is to be chosen from 8 batsmen and 5 bowlers. In how many ways can the team be chosen so as to include at least 3 bowlers?

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A cricket team consist of 11 players is to be chosen from 8 batsmen and 5 bowlers. In how many ways can the team be chosen so as to include at least 3 bowlers?

Asked by arnavmohanty1999 11th April 2017, 5:46 PM
Answered by Expert
Answer:

begin mathsize 16px style Given space that space 11 space players space is space to space be space chosen space from space 8 space batsman space and space 5 space bowler space such space as space at space least space 3 space bowlers space will space included.
This space means space we space can space have space 3 space bowlers space or space 4 space bowlers space or space 5 space bowlers.
We space will space make space cases space such space as comma
straight i right parenthesis space 3 space bowlers space and space 8 space batsmen
rightwards double arrow straight C presuperscript 5 subscript 3 cross times straight C presuperscript 8 subscript 8
ii right parenthesis space 4 space bowlers space and space 7 space batsmen
rightwards double arrow straight C presuperscript 5 subscript 4 cross times straight C presuperscript 8 subscript 7
iii right parenthesis space 5 space bowlers space and space 6 space batsmen
rightwards double arrow straight C presuperscript 5 subscript 5 cross times straight C presuperscript 8 subscript 6
Adding space these space three space we space get space required space answer comma
straight C presuperscript 5 subscript 3 cross times straight C presuperscript 8 subscript 8 plus straight C presuperscript 5 subscript 4 cross times straight C presuperscript 8 subscript 7 plus straight C presuperscript 5 subscript 5 cross times straight C presuperscript 8 subscript 6 equals 10 plus 5 cross times 8 plus 28 equals 10 plus 40 plus 28 equals 78
end style

Answered by Expert 11th April 2017, 5:55 PM
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