Question

A team of 8 players is to be chosen from a group of 12 players. Out of the eight players one is to be elected as captain and another as vice-captain. In how many ways can this be done?

(a) 27720

(b) 13860

(c) 6930

(d) 495

Answer 1

Correct option is (a) 27720

Number of ways to choose 8 players from 12 players

= \(^{12} C_8 = \frac{12!}{8!4!} = 495\)

Number of ways to choose a captain and a vice captain

= ⁸C₁ × ⁷C₁

= 8 × 7

= 56

∴ Required number of ways = 495 × 56 = 27720