In how many different ways can you arrange five flags in a row if there are two red flags and three blue flags?

Question

In how many different ways can you arrange five flags in a row if there are two red flags and three blue flags?

Answer 1

if all the flags were distinct, each flag being a different color, there would be 5! different arrangements

now determine how many times each arrangement is repeated

2 red flags can be done in 2! ways if they were all different colors

3 blue flags can be done in  3! ways if they were all different colors

divide the total number of arrangements (5!) by the total number of repetitions

5!/(3!*2!)

simplifying

5*4/2=20/2=10 ways