Question

Could somebody PLEASE help with this question?

The coach from a soccer team of 15 players must select 11 players for the start of a game.
a) Of the 11 players he must select 1 player as the field captain. How many ways can the coach make these selections?

b) Before the game all players line up in a straight line for a team photograph. If 2 players, Michaela and Aleah must be together, then how many different arrangements can be made for the picture?

Answer 1

a) There are 15C11 ways of selecting the team. Having selected the team, there are 11 choices for the captain.
The total number of ways of selecting the team and the captain is:

`15C11*11=15015`

b) The number of different arrangements for the picture are:

`10!*2=7257600`

Answer 2

Answer: a) 15015

b) 87,178,291,200

Explanation:

Since we have given that

Number of players in a soccer team = 15

Number of players for the start the game = 11

Out of 11 players, the number of player as the field captain = 1

So, Number of ways that the coach make these selections is given by

`^(15)C_(11)* ^(11)C_1\\\\=1365* 11\\\\=15015`

b) Before the game all players line up in a straight line for a team photograph. If 2 players, Michaela and Aleah must be together.

So, MA would be together.

So, Consider MA be 1 unit.

so, remaining members = 15-2 = 13

Total members after including MA as 1 unit = 14

Number of arrangements that can be made for the picture would be

`14* 13!\\\\=87178291200`