SOLUTION: A particular level of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order. There are 3 red towers, 5 grey towers, and 2 green towers to

Algebra ->  Permutations -> SOLUTION: A particular level of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order. There are 3 red towers, 5 grey towers, and 2 green towers to      Log On


   

Question 636931: A particular level of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order. There are 3 red towers, 5 grey towers, and 2 green towers to choose from for this level. How many different arrangements of towers are possible?
My thinking is 3! * 5! * 2! Am I on the right track?
Thank you in advance for any assistance.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A particular level of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order. There are 3 red towers, 5 grey towers, and 2 green towers to choose from for this level. How many different arrangements of towers are possible?
My thinking is 3! * 5! * 2! Am I on the right track?
-----
If the towers of the same color are distinguishable you get
3! = 6 ways to arrange the color groups
3! ways to arrange the red
5! ways to arrange the grey
2! ways to arrange the green
Total arrangements: 6*3!*5!*2! = 8640
-----------------------------------------------
---
If those of the same color are not distinguishable the answer
would be 10!/(3!*5!*2!) = 2520 arrangements
------------------------------------------------
Cheers,
Stan H.