Question 1163310: In their kindergarten classroom, a child is pouring and layering different colors of sand into a jar to create a mother’s day gift. There are 7 colored sands to choose from. The child is only allowed to use 4 colors, one for each of the four layers. How many different layer combinations are there if the top layer must be purple and the bottom layer must be red, and each layer must be a separate color?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! In their kindergarten classroom, a child is pouring and layering different
colors of sand into a jar to create a mother’s day gift. There are 7 colored
sands to choose from. The child is only allowed to use 4 colors, one for
each of the four layers. How many different layer combinations are there if
the top layer must be purple and the bottom layer must be red, and each
layer must be a separate color?
We only need to figure the colors for the middle two layers. There are only
5 colors left to choose from for the middle two layers (since purple and red
must be used for the top and bottom layers, and the colors must all be
different).
A child can choose a color for the upper middle layers in 5 ways.
A child can then choose a color for the lower middle layer in 4 ways.
Answer: 5∙4 = 20 ways.
Edwin
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