Question

How many distinct signals can be made with 8 flags displayed at the same time in a vertical array if 3 flags are white, 2 flags are red, 1 flag is checkered and the rest of the flags are yellow?

Answer 1

Suppose all \(8\) flags are of different colors, then the number of distinct signals is simply
\[8!\]

However thats not the case here. We have duplicates : \(3\) whites, \(2\) red, \(2\) yellow. changing the positions among \(3\) whites wont produce a new signal and there are \(3!\) such duplicates for whites, \(2!\) duplicates for red and \(2!\) duplicates for yellow.
Divide these duplicates to get the total number of distinct signals that can be made
\[\dfrac{8!}{3!\cdot 2!\cdot 2!}\]

Answer 2

thank you I understand now

Answer 3

yw!