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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

1 Answer

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Best 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.

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