In how many ways, a captain of a cricket team can be selected within 11…
2025
In how many ways, a captain of a cricket team can be selected within 11 players from a squad of 14 players?
- A.
4004
- B.
1001
- C.
364
- D.
264
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Solution
We must pick an 11-player team from 14 players and designate one of those 11 as captain.
Method 1: Choose the 11-player team first.
Number of teams = C(14,11) = 364. For each team choose a captain in 11 ways, so total = 364 × 11 = 4004.
Method 2 (equivalent): Choose the captain first.
Choose captain: 14 ways. Then choose the remaining 10 players from the other 13: C(13,10) = 286. Total = 14 × 286 = 4004.
Final answer: 4004