Question

A lot of national flags are made up of three horizontal stripes.

Answer 1

How many different three colour flags (tricolors) can be designed using green, blue, red, yellow and black stripes if all three colours must be different?
6P3 = 6!/(6 - 3)! = 6!/3! = (6 x 5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 720/6 = 120 flags.

How many of them contain a red stripe?
The remaining two colours can be arranged in 5P2 = 5!/(5 - 2)! = 5!/3! = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 120/6 = 20ways
The red stripe can arranged in 3 ways
Therefore, number of flags having red stripe is 20 x 3 = 60 flags.