In how many ways can one select a cricket team of eleven from

Out of 17 players, 5 players are bowlers.

A cricket team of 11 players is to be selected in such a way that there are exactly 4 bowlers.

4 bowlers can be selected in ${ }^{5} \mathrm{C}_{4}$ ways and the remaining 7 players can be selected out of the 12 players in ${ }^{12} \mathrm{C}_{7}$ ways.

Thus, by multiplication principle, required number of ways of selecting cricket team  

$={ }^{5} \mathrm{C}_{4} \times{ }^{12} \mathrm{C}_{7}=\frac{5 !}{4 ! 1 !} \times \frac{12 !}{7 ! 5 !}=5 \times \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}=3960$