In how many ways a cricket team of eleven be selected from 17 players in which 5 players are bowlers and the cricket team must include 2 bowlers?

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Solution

Selecting $11$ out of $17$
$5$ bowlers $⟶$ select $2$ bowlers
$12$ batsman $⟶$ $9$ to be selected
Number of ways of selecting two bowlers $=^{5} C_{2} = 10$
Number of ways of selecting rest
$\Rightarrow^{12} C_{9} \Rightarrow \frac{12 \times 11 \times 10}{3 \times 2 \times 1} \Rightarrow 220$
Total ways $= 10 \times 220 = 2200$
Hence the correct answer is $2200$ ways

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In how many ways a cricket team of eleven be selected from 17 players in which 5 players are bowlers and the cricket team must include 2 bowlers?

Selecting 11 out of 175 bowlers ⟶select 2 bowlers12 batsman⟶ 9 to be selected Number of ways of selecting two bowlers=5C2=10Number of ways of selecting rest ⇒12C9⇒12×11×103×2×1⇒220Total ways =10×220=2200Hence the correct answer is 2200 ways