In how many ways $11$ players can be selected from $15$ players, if only $6$ of these players can bowl are the $11$ players must include atleast $4$ bowlers?

1170

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1422

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2361

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None of these

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Solution

The correct option is C $2361$
Case $1 :$ Exactly $4$ bowlers $.$
Four bowlers can be select from the $6$ bowlers and seven players can be selected from $9$ players $(15 - 6 = 9)$ is the no $:$ of selecting the cricket eleven $,$
$P = C (5, 4) \times C (9, 4) =^{6} C_{4} \times^{9} C_{4} = 540$
Case $2 :$ Having $5$ bowlers out of $6.$
$P = C (6, 5) \times C (9, 6) =^{6} C_{5} \times^{9} C_{5} = 378$
$∴$ No $:$ of ways they can be selected $= 540 + 504 + 378 = 1422$ ways $.$

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In how many ways 11 players can be selected from 15 players, if only 6 of these players can bowl are the 11 players must include atleast 4 bowlers?

In how many ways $11$ players can be selected from $15$ players, if only $6$ of these players can bowl are the $11$ players must include atleast $4$ bowlers?