A team of 8 players has to be selected from 14 players. In how many wa

1.	A team of 8 players has to be selected from 14 players. In how many ways the selections can be made if (a) Two particular players are always included. (b) Two particular players are always excluded.
Answer» (a) Two players are always included: We have to choose 6 from 12 players. This can be done in ¹²C₆ ways = 924 ways. (b) Two players are always excluded: We have to choose 8 from 12 players. This can be done in ¹²C₈ ways = 495 ways.

A team of 8 players has to be selected from 14 players. In how many ways the selections can be made if (a) Two particular players are always included. (b) Two particular players are always excluded.

Answer»

(a) Two players are always included:

We have to choose 6 from 12 players. This can be done in ¹²C₆ ways = 924 ways.

(b) Two players are always excluded:

We have to choose 8 from 12 players. This can be done in ¹²C₈ ways = 495 ways.