Question

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them, is
(a) ¹⁶C₁₁
(b) ¹⁶C₅
(c) ¹⁶C₆
(d) ²⁰C₉

Answer 1

Total number of players = 22
We need to select 11 players
Given condition says,
Exclude 4 particular player gives us 18 players available and including 2 particular players.
Implies only 9 need to be selected out of remaining 16.
Hence, number of ways of selection is ¹⁶C₉.
Hence, the correct answer is option C.