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# Counting and Probability Question

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My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are interchangeable). How many different starting lineups can I choose?

Aug 6, 2022

#1
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The goali is the same, whatever team You chose. So we have 10 from 15. \(\binom{15}{10} = 3003\)

Aug 6, 2022
edited by tuffla2022  Aug 6, 2022
edited by tuffla2022  Aug 6, 2022
#2
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Hi Tuffla2022,

Welcome to our forum

I see you have already contributed a lot of good quality answers.

Knowing how soccer is played I am sure your answer, in the real world, wold be correct.

However,

I have interpreted it differently.

I don't think you should assume that everyone answering this question knows the rules of soccer.

The info that you need should be in the question.

So i have assumed that the goalie can be any of the 16 players.

Choose the 11 playrers and then chose the goalie from them

16C11 *10 = 4368 * 11 = 48048

or

Chose the goalie and then choose the 10 players.

16*15C10 = 16 * 3003 =  48048

Aug 7, 2022
edited by Melody  Aug 7, 2022