A cricket team has 15 members,of whom only 5 | vedclass

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(C) Total members = $15$,Bowlers = $5$,Non-bowlers = $10$. We need to select $11$ members such that at least $3$ are bowlers.The total number of ways

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$\frac{12}{13}$

Vedclass · Answer

(C) Total members = $15$,Bowlers = $5$,Non-bowlers = $10$. We need to select $11$ members such that at least $3$ are bowlers.The total number of ways to select $11$ members from $15$ is $^{15}C_{11} = ^{15}C_{4} = \frac{15 	imes 14 	imes 13 	imes 12}{4 	imes 3 	imes 2 	imes 1} = 1365$.The number of ways to select at least $3$ bowlers is:Case $1$: $3$ bowlers and $8$ non-bowlers: $^{5}C_{3} 	imes ^{10}C_{8} = 10 	imes 45 = 450$.Case $2$: $4$ bowlers and $7$ non-bowlers: $^{5}C_{4} 	imes ^{10}C_{7} = 5 	imes 120 = 600$.Case $3$: $5$ bowlers and $6$ non-bowlers: $^{5}C_{5} 	imes ^{10}C_{6} = 1 	imes 210 = 210$.Total favorable ways = $450 + 600 + 210 = 1260$.Probability = $\frac{1260}{1365} = \frac{12}{13}$.

$A$ cricket team has $15$ members,of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ are drawn at random,then the probability of obtaining a team of $11$ containing at least $3$ bowlers is

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