Question

. Suppose you are a coaching a team of 9-year-old soccer players and need to figure out a starting line-up. You have 17 players on the team. For younger players, they play with only 6 players at a time. If the kids just go out as a group and play without positions being assigned, how many different 6-person groups do you have to choose from when deciding who will start the game?

6. Now suppose that your team (from problem 5) is a little older and positions do matter. You still will have only 6 of the 17 players playing at any given time. How many different 6-person teams do you have to choose from now that each player will be assigned a specific position?

Answer 1

Question (1)

Given that there are 17 players and we need to select 6 players and without position being assigned

In simple statistical ordering is not important

So We just select 6 players from total 17 players which can be in = 17! / 6! * (17-6)!

= 17 ! / 6! * 11!

= 12376

Number of different 6-person groups to choose from when deciding who will start the game = 12376

Question (2)

Given that there are 17 players and we need to select 6 players and each player is assigned a specific position

In simple statistical ordering is important

The 6 selected players can be assigned to a specific posotion in 6*5*4*3*2*1 6! which is 6! ways as 1st player can be assigned to any of 6 positions, 2nd player can be assigned to any of remaining 5 positions, 3rd player can be assigned to any of remaining 4 positions, 4th player can be assigned to any of remaining 3 positions, 5th player can be assigned to any of remaining 2 positions, 6h player can be assigned to remaining 1 position

So we select 6 players from 17 players and also assign them to a specific poostion which can be in * 6!

= [17! / 6! * (17-6)! ] * 6!

= 17! / 11!

= 8910720 ways

Number of different 6-person teams to choose from now that each player will be assigned a specific position = 8910720