There are 13 players of cricket, out of which 4 are bowlers.
Question:

There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?

(a) 72

(b) 78

(c) 42

(d) none of these

Solution:

(b) 78

4 out of 13 players are bowlers.

In other words, 9 players are not bowlers.

A team of 11 is to be selected so as to include at least 2 bowlers.

$\therefore$ Number of ways $={ }^{4} C_{2} \times{ }^{9} C_{9}+{ }^{4} C_{3} \times{ }^{9} C_{8}+{ }^{4} C_{4} \times{ }^{9} C_{7}$

$=6+36+36$

$=78$