SOLUTION: Emily has been asked to set up the display of new shirts that just arrived at the store where she works. There are 9 different colors of shirts. a. How many different ways can s

Question 1118876: Emily has been asked to set up the display of new shirts that just arrived at the store where she works. There are 9 different colors of shirts.
a. How many different ways can she arrange the shirts?
b. How many different ways can she arrange the shirts if the first one has to be yellow and the third one has to be blue?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I choose to answer your second question.

There is one way to choose the first shirt, namely the yellow one. There are 7 ways to choose the second shirt, namely one of the seven colors that is not yellow and is not blue. So there are 7 possibilities for the first two shirts. Then there is one way to choose the third shirt, namely the blue one. So there are 7 ways (1 times 7 times 1) ways to choose the first three shirts. Then, for each of those 7 ways, there are 6 ways to choose the color of the 4th shirt, namely one of the six shirts that is not yellow, not blue, and not the color that was chosen for the 2nd shirt. So, 1 times 7 times 1 times 6 = 42 ways to choose the colors for the first four shirts. Then 5 ways for the 5th shirt, and so on.

John

My calculator said it, I believe it, that settles it

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