In how many ways can a team of 11 players be selected from 14 players

1.	In how many ways can a team of 11 players be selected from 14 players when two of them play as goalkeepers only?(a) 112 (b) 132 (c) 91 (d) 182
Answer» (b) 132 As each team of 11 players has one goalkeeper and 10 team members, and out of 14 players there are 2 goalkeepers and 12 team members. So the number of ways in which a team of 11 can be selected = ¹²C₁₀ x ²C₁ \(\frac{12!}{10!\times2!}\times2\) = \(\frac{12\times11}{2}\times2\) = 132.

In how many ways can a team of 11 players be selected from 14 players when two of them play as goalkeepers only?(a) 112 (b) 132 (c) 91 (d) 182

Answer»

(b) 132

As each team of 11 players has one goalkeeper and 10 team members, and out of 14 players there are 2 goalkeepers and 12 team members.

So the number of ways in which a team of 11 can be selected

= ¹²C₁₀ x ²C₁ \(\frac{12!}{10!\times2!}\times2\)

= \(\frac{12\times11}{2}\times2\) = 132.