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Homework Statement
We want to put 4 Maroon, 3 Green, and 2 Yellow plates in a row on a table. They are arranged randomly. What is the probability that the 4 Maroon plates are together?
Homework Equations
The Attempt at a Solution
I couldn't figure out how to set this problem up properly.
All I could think to do was to break it into the six outcomes we are interested in.
Let X denote a non-maroon plate and M denote a maroon plate.
So the outcomes are:
1- M M M M X X X X X
2- X M M M M X X X X
3- X X M M M M X X X
4- X X X M M M M X X
5- X X X X M M M M X
6- X X X X X M M M M
P(1) = (4/9)(3/7)(2/6)(1/5) = 1/126
P(2) = (5/9)(4/8)(3/7)(2/6)(1/5) = 1/126
P(3) = (5/9)(4/8)(4/7)(3/6)(2/5)(1/5) = 1/126
P(4) = ... = 1/126
P(5) = ... = 1/126
P(6) = ... = 1/126
So for a final answer I get 1/21. I'm not very confident in that answer, plus there has to be some way to set this up much simpler. Using the (n choose k) deal..
Any advice would be awesome.
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