Question

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

Answer 1

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