There are 15 players in a cricket team,out of | vedclass

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(C) Total players = $15$ ($6$ Bowlers,$7$ Batsmen,$2$ Wicketkeepers). We need to select $11$ players such that there are at least $4$ bowlers,$5$ bats

Vedclass · Accepted Answer

$777$

Vedclass · Answer

(C) Total players = $15$ ($6$ Bowlers,$7$ Batsmen,$2$ Wicketkeepers). We need to select $11$ players such that there are at least $4$ bowlers,$5$ batsmen,and $1$ wicketkeeper. The possible cases for (Bowlers,Batsmen,Wicketkeepers) are: $1$. $(4, 5, 2): {}^{6}C_{4} 	imes {}^{7}C_{5} 	imes {}^{2}C_{2} = 15 	imes 21 	imes 1 = 315$ $2$. $(4, 6, 1): {}^{6}C_{4} 	imes {}^{7}C_{6} 	imes {}^{2}C_{1} = 15 	imes 7 	imes 2 = 210$ $3$. $(5, 5, 1): {}^{6}C_{5} 	imes {}^{7}C_{5} 	imes {}^{2}C_{1} = 6 	imes 21 	imes 2 = 252$ Summing these up: $315 + 210 + 252 = 777$. Thus,the total number of ways is $777$.

There are $15$ players in a cricket team,out of which $6$ are bowlers,$7$ are batsmen,and $2$ are wicketkeepers. 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 $1$ wicketkeeper is $.....$

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