In a touring cricket team,there are 16 player | vedclass

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(B) Total players = $16$. Bowlers = $5$,Wicket-keepers = $2$,Others = $16 - (5 + 2) = 9$. We need to select $11$ players including $3$ bowlers and $1$

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(B) Total players = $16$. Bowlers = $5$,Wicket-keepers = $2$,Others = $16 - (5 + 2) = 9$. We need to select $11$ players including $3$ bowlers and $1$ wicket-keeper. Number of ways to select $3$ bowlers from $5$ = $^5C_3 = \frac{5 	imes 4}{2 	imes 1} = 10$. Number of ways to select $1$ wicket-keeper from $2$ = $^2C_1 = 2$. Remaining players to be selected = $11 - (3 + 1) = 7$. These $7$ players must be selected from the remaining $9$ players = $^9C_7 = ^9C_2 = \frac{9 	imes 8}{2 	imes 1} = 36$. Total number of ways = $10 	imes 2 	imes 36 = 720$.

In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that the team includes exactly $3$ bowlers and $1$ wicket-keeper?

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