Question

you have 15 players. you need to pick 11

1-no restriction on who plays

2-one player must always be chosen

2 one player is never chosen

Answer 1

Let n = number of players = 15

m = number of player to be chosen = 11.

1) Without restriction the number of ways to choose 11 players from 15 player in ¹⁵ C₁₁ ways.

=

Without restriction, total number of ways to select 11 players from 15 players in 1365 ways.

2) One player must always be chosen.

We fixed 1 player and remaining 10 players select from 14 players in ¹⁴ C₁₀ ways.

total number of ways = 1001

3) One player never be chosen.

We remove one player from 15 players. To select 11 players from remaining 14 players in ¹⁴ C₁₁ ways.

total number of ways = 364.