Final answer:
The number of ways to select a cricket team with 4 bowlers from 17 players is C(17,11) × C(12,7).
Step-by-step explanation:
To select a cricket team of eleven from 17 players in which only 5 players can bowl, and each team must include exactly 4 bowlers, we can use the combination formula. The number of ways to select 4 bowlers from 5 players is C(5,4) = 5. The number of ways to select the remaining 7 players from the remaining 12 non-bowlers is C(12,7) = 792. Therefore, the total number of ways to select the cricket team is C(17,11) × C(5,4) × C(12,7).
To determine how many ways one can select a cricket team of eleven from 17 players where only 5 can bowl and each team must include exactly 4 bowlers, we can use combinations. Since there are 5 bowlers and we need 4 in the team, we select 4 bowlers from the 5 available.
This gives us C(5,4) possibilities. Then, we need to select the remaining 7 players from the 12 who are not bowlers, which gives us C(12,7) possibilities. The total number of ways to select the team is the product of these two combinations, which is C(5,4) × C(12,7).
So, the correct option is (b) C(17,11) × C(12,7).