A picture perfect permutation problem

gbecker360

New member
Joined
Jan 25, 2018
Messages
1
We were doing some permutations in class today, teacher left us with one for homework that had me stumped.:(
Our class was asked to find the best formula for modelling the following problem:

A photographer is taking a photo of a soccer team. There are 15 players in total: 2 coaches, 6 defenders, 6 forwards and 1 goalkeeper. The photographer has a specific arrangement for the players, with the coaches on either side of the defenders in the back row, and the goalie front and centre with 3 forwards on either side.
The question had a diagram similar to this:

C D D D D D D C
...F F F G F F F

A friend told me that because of the repeated letters, the formula would be: 15! / (2!6!6!)
I wasn't sure this was correct as the question deals with individual players, unlike letters in a word problem, the answer would just be: 2!6!6!

Who's right? Or are we both overlooking the obvious...;)

P.S. This is my first post, is there a way of entering equations like there is in word?
 
Last edited by a moderator:
… is there a way of entering equations like there is in word?
The LaTex formatting system for math is available here. It's not menu-driven, like the equation editor in MSWord; users need to learn some code.

You'll find a little more information about LaTex in this post. :cool:

By the way, if you want to use repeated spaces in this forum to align or position things, you'll need to use the code tags and choose the Courier New font (fixed-width). Otherwise, the forum software strips out repeated spacing.
 
A photographer is taking a photo of a soccer team. There are 15 players in total: 2 coaches, 6 defenders, 6 forwards and 1 goalkeeper. The photographer has a specific arrangement for the players, with the coaches on either side of the defenders in the back row, and the goalie front and centre with 3 forwards on either side.
The question had a diagram similar to this:

C D D D D D D C
...F F F G F F F

A friend told me that because of the repeated letters, the formula would be: 15! / (2!6!6!)
I wasn't sure this was correct as the question deals with individual players, unlike letters in a word problem, the answer would just be: 2!6!6!

Who's right? Or are we both overlooking the obvious...

As you say, the friend's formula would be what you'd use if you were asked how many ways there are to arrange the LETTERS, ignoring which individual is in each place. This problem is sort of the opposite: the letters are in fixed positions, and you are to pay attention only to the arrangement of the individuals who go in those places. So your answer is correct: 2! ways to arrange the 2 coaches, 6! ways to arrange the defenders, 6! for the forwards, and 1 for the goalkeeper. Good work!
 
Top