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

Answer 1

(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.

$$\begin{gathered} \therefore \mathrm{Number}\mathrm{of}\mathrm{ways}{=}^4{C}_2{\times }^9{C}_9+{}^4{C}_3{\times }^9{C}_8+{}^4{C}_4{\times }^9{C}_7 \\ =6+36+36 \\ =78 \end{gathered}$$