Question

In a touring cricket team there are 16 players in all including 5 bowlers and 2 wicket-keepers. How many teams of 11 players from these, can be chosen, so as to include three bowlers and one wicket-keeper

• A. 720
• B. 840
• C. 600
• D. 960

Answer 1

Answer: (A)

720

Answer 2

1. Calculate the number of players who are neither bowlers nor wicket-keepers: 16 total players - (5 bowlers + 2 wicket-keepers) = 9 players.
2. Determine the composition of the 11-player team: 3 bowlers, 1 wicket-keeper, and 11 - 3 - 1 = 7 other players.
3. Calculate the number of ways to select players from each category using combinations (${}^{n}{{C}_{r}} = \dfrac{n!}{r!(n-r)!}$):
   • Ways to choose 3 bowlers from 5: ${}^{5}{{C}_{3}} = 10$
   • Ways to choose 1 wicket-keeper from 2: ${}^{2}{{C}_{1}} = 2$
   • Ways to choose 7 other players from 9: ${}^{9}{{C}_{7}} = 36$
4. Multiply these numbers to find the total number of ways to form the team: $10 \times 2 \times 36 = 720$.