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