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

Question

asked Sep 26, 2023 136k views

1 Answer

Dan Watt · Answer 1 · 2023-09-30T14:47:43+0000

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