Question

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? *the answer is not 4368*

Answer 1

Answer:

3003

Step-by-step explanation:

We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)

The number of different lineups you can have can be found by using combination:

$^{15}C_{10} = \frac{15!}{(15 - 10)! 10!}\\ \\= \frac{15!}{5! * 10!} \\\\= 3003$

There are 3003 different lineups that can be chosen.