Q. 4

In how many ways can a football team of 11 players be selected from 16 players? How many of these will (i) include 2 particular players? (ii) exclude 2 particular players.

Answer :

Given that we need to choose 11 players for a team out of available 16 players,


Let us assume the choosing the no. of ways be N,


N = choosing 11 players out of 16 players


N = 16C11


We know that


And also n! = (n)(n – 1)(n – 2)…………2.1





N = 4368 ways


(i) It is told that two players are always included.


It is similar to selecting 9 players out of the remaining 14 players as 2 players are already selected.


Let us assume the choosing the no. of ways be N1,


N1 = choosing 9 players out of 14 players


N1 = 14C9


We know that


And also n! = (n)(n – 1)(n – 2)…………2.1





N1 = 2002 ways


(ii) It is told that two players are always excluded.


It is similar to selecting 11 players out of the remaining 14 players as 2 players are already removed.


Let us assume the choosing the no. of ways be N2,


N2 = choosing 11 players out of 14 players


N2 = 14C11


We know that


And also n! = (n)(n – 1)(n – 2)…………2.1





N2 = 364 ways


The required no. of ways are 4368, 2002, 364.


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