Question

we design a new flag.they are 5 colors,blue,red,green,orange and yellow.the flag must have 3 bands of color,how many different flags can be design ?

Answer 1

If it is okay to have blue green red and red green blue as a different flag...then you will have 60 possible flags. For the first stripe you have 5 choices, for the second 4 choices and for the last 3 choices = 60 flags.

If you cannot have the same colors in a different order than you will have only 10 possibilities. Use the Combination rule of 5 factorial divided by (3 factorial times 3 factorial). 5 factorial means 5X4X3X2X1 =120 divided by (3x2x1)(2x1) so you have 120/12 = 10.