Question

A soccer coach assigns his players randomly, 1 as a goalie, 4 as defenders, 3 as midfielders, and 3 as forwards. (a) How many choices does he have? (b) IF only one player is experienced enough to play as a goalie, what is the probability that in the random division, he end up to be the goalie?

Answer 1

a)

number of ways to assign 11 player to groups of 1,4,3 and 3 =11!/(1!*4!*3!*3!) =46200

b)

number of ways the person with experience as goalie be assigned as goalie =arrange remaining 10 players in groups of 4,3 and 3=10!/(4!*3!*3!) =4200

therefore P( in the random division, he end up to be the goalie ) =4200/46200=1/11

(Note: this can be solved simply as 1/11 (since out of 11 position he is experienced for as a goalie which is 1 position)