Question

How many different arrangements of the letters in the word "PURPLE" are there? a)30 b)360 c)720

Answer 1

how many letters are there

Answer 2

6

Answer 3

so if you had 6 distinct letters, then you would have 6! = 6*5*4*3*2*1 = 720 different ways to arrange them

BUT

you have two copies of P that are indistinguishable, so we double counted when we got 720, which is why we must divide by 2 to get 720/2 = 360

Answer 4

I see thanks @jim_thompson5910

Answer 5

yw