SOLUTION: I have 5 pictures, picture "A" must remain in the center. How many possible combinations/arrangements can be made with the four other pictures (b, c, d, e)?

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Question 239606: I have 5 pictures, picture "A" must remain in the center. How many possible combinations/arrangements can be made with the four other pictures (b, c, d, e)?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


I presume that you are making a single row of pictures with A in the center.

So the pictures must end up in the following arrangement:

X X A X X

There are 4 ways to choose the first picture. For each of those ways, there are three ways to pick the second picture. So there are 4 times 3 = 12 ways to pick the first two pictures. The third picture is fixed, so that doesn't change anything, and there are still 12 ways to choose the first three pictures. For each of those ways there are 2 ways to pick the 4th picture, so 12 X 2 = 24 ways to pick the first 4. Then there is 1 way to pick the last one. so 24 X 1 = 24. Total of 24 ways.

John
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