+140 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?
+113 The goali is the same, whatever team You chose. So we have 10 from 15. \(\binom{15}{10} = 3003\)
See https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php
+118687 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
