Question

The number of ways a cricket team of 11 players be chosen out of 15 players of whom 6 are bowlers if the team consists of atleast 5 bowlers

• A. 630
• B. 504
• C. 126
• D. 526

Answer 1

Answer: (A)

630

A cricket team of 11 players be chosen out of 15 players of whom 6 are bowlers if the team consists of at least 5 bowlers. So the Number of batsman$=15-6=9$

So the Number of cases are as follows

Bowlers(6) Batsmen(9)

5 6

6 5

So for the first case ${}^6{C}_5{\times }^9{C}_6$

For the second Case${=}^6{C}_6{\times }^9{C}_5$

Total Cases${=}^6{C}_5{\times }^9{C}_6{+}^6{C}_6{\times }^9{C}_5=504+126=630$