Question

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

Answer 1

Answer: 360

Explanation:

Given word : PURPLE

The number of letters in the word (n)=6

Since P is repeating two times in the given word.

Therefore, the number of possible arrangements of the letters in the word "PURPLE"

`=(6!)/(2!)\\\\=(6*5*4*3*2*1)/(2)\\\\=(720)/(2)\\\\=360`

Hence, there are 360 different arrangements of the letters in the word "PURPLE" .

Answer 2

there are 6 letters

6 x 5 x 4 x3 x 2= 720

there are 2 P's

so 720/2 = 360

there are 360 possible arrangements