Question

The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

• A. 165
• B. 364
• C. 1001
• D. 1365

Answer 1

Answer: (C)

1001

Total number of selection of $11$ players out of $15$ players in which captain is included $={}^{14}{C}_{10}$

$=\frac{14!}{10!4!}=\frac{14\times 13\times 12\times 11}{1\times 2\times 3\times 4}=1001$

Hence, C is the correct option.