In how many ways can one select a cricket team of eleven from $14$ players in which only $4$ players can bowl if each cricket team of $11$ must include exactly $2$ bowlers?

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Solution

No. of players required $= 11$
No. of available players $= 14$
No. of players who can bowl $= 4$
No. of players who can't bowl $= 10$
No. of bowler required in team $= 2$
No. of ways of selecting a bowler $= 4_{c_{2}}$
No. of ways of selecting a player who can't bowl $= 10_{c_{9}}$
No. of ways a team can be made $= 4_{c_{2}} \times 10_{c_{9}}$
$= 6 \times 10 = 60$ ways

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