In a group of 13 cricket players, four are bowlers. Find out in how many ways can they form a cricket team of 11 players in which at least 2 bowlers are included.

Question

In a group of 13 cricket players, four are bowlers. Find out in how many ways can they form a cricket team of 11 players in which at least 2 bowlers are included. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6da717486aa3d73432c90ef1e784b56e-.png" /> ⇒ 4 C 2 × 9 C 9+ 4 C 3 × 9 C 8+ 4 C 4 × 9 C 7 =6+36+36=78

Q. In a group of $13$ cricket players, four are bowlers. Find out in how many ways can they form a cricket team of $11$ players in which at least $2$ bowlers are included.

$\Rightarrow^{4} C_{2} \times^{9} C_{9} +^{4} C_{3} \times^{9} C_{8} +^{4} C_{4} \times^{9} C_{7}$
$= 6 + 36 + 36 = 78$

Q. In a group of 13 cricket players, four are bowlers. Find out in how many ways can they form a cricket team of 11 players in which at least 2 bowlers are included.

⇒4C2​×9C9​+4C3​×9C8​+4C4​×9C7​ =6+36+36=78

Q. In a group of $13$ cricket players, four are bowlers. Find out in how many ways can they form a cricket team of $11$ players in which at least $2$ bowlers are included.

$\Rightarrow^{4} C_{2} \times^{9} C_{9} +^{4} C_{3} \times^{9} C_{8} +^{4} C_{4} \times^{9} C_{7}$
$= 6 + 36 + 36 = 78$