Permutation and Combination - Selections with Restrictions
Permutation and Combination - Selections with Restrictions
A coach has, in his soccer team, \(5\) strikers, \(8\) midfielders, \(9\) defenders and \(3\) goalkeepers. He has to select exactly \(1\) goalkeeper and \(10\) other players to start a match.
- in how many ways can he select the \(11\) players,
- in each of the four sections (goalkeepers, strikers, defenders and midfielders), there is one STAR player. How many ways can the coach choose his \(11\) players if he must include at least one STAR player?
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Answer:(i) \(1\,939\,938\) (ii) \(1\,755\,182\)
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