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Suppose we want to choose 5 colors, without replacement, from 8 distant colors.

User Ioan M
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1 Answer

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When the order is relevant


8P5=(8!)/((8-5)!)=(8!)/(3!)=8\cdot7\cdot6\cdot5\cdot4=6720

When the order it is no relevant:

We get that this problem is equivalent to say "how many ways are to choose 5 from a group of 8" so the answer is


8C5=(8!)/((8-5)!\cdot5!)=(8!)/(3!\cdot5!)=(40320)/(6\cdot120)=56

so there are 56 ways to choose 5 colors from 8 without replacement

User Dan Watt
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