Question

A team of 8 players is to be chosen from a group of 12 players. Out of the 8 players one is to be elected as captain and another an, vice-captain. In how many ways can this is done? (A) 27720 (B) 13860 (C) 6930 (D) 495

Answer 1

Number of ways selecting `8` players out of `12` players `= C(12,8)`
Number of ways selecting `1` captain out of `8` selected players `= C(8,1)`
Number of ways selecting `1` vice-captain out of `7` remaining players `= C(7,1)`
So, total number of ways to do all above selection `= C(12,8)**C(8,1)**C(7,1) = (12**11**10**9)/(4**3**2)**8**7 = 495**56 = 27720`