Question

A cricket team of 11 players is to be formed from 16 players including 4 bowlers and 2 wicket keepers. In how many different ways can a team be formed so that the team has at least 3 bowlers and at least one wicket keeper?

• A. 2472
• B. 2274
• C. 2427
• D. 1236

Answer 1

The correct option is A 2472

Total number of bowlers = 4
Total number of wicket keepers = 2
Rest (normal) players = 10
Possible Combinations:
$\begin{array}{ccc}Bowlers& Wicketkeepers& Normalplayers\\ 3& 1& 7\\ 3& 2& 6\\ 4& 1& 6\\ 4& 2& 5\end{array}$
$\therefore$ Required number of ways
${(}^4{C}_3{\times }^2{C}_1{\times }^{10}{C}_7)+{(}^4{C}_3{\times }^2{C}_2{\times }^{10}{C}_6)+{(}^4{C}_4{\times }^2{C}_1{\times }^{10}{C}_6)+{(}^4{C}_4{\times }^2{C}_2{\times }^{10}{C}_5)=(4\times 2\times 120)+(4\times 1\times 120)+(1\times 2\times 210)+(1\times 1\times 252)=960+840+420+252=2472$