In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

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 ⁵C₄ ways and the remaining 7 players can be selected out of the 12 players in ¹²C₇ ways.

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

⁵C₄ × ¹²C₇ = (5! / (4! × 1!)) × (12! / (7! × 5!))

= 5 × (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1) = 3960

Hence, the required number of ways = 3960.