Question

How many different arrangements of the letters in the word PARALLEL are there?

56
3,360
40,320

Answer 1

total number of words ,n= 8
a occurs two times
l occurs 3 times

8! is basically arranging the 8 letters, but it implies that substituting the 2 a's in 'parallel' is a different permutation. Since there are 2! ways to arrange the a's among themselves, and 3! ways to arrange the 3 l's as well, you must divide them to the original permutation (which is 8!) to get the more realistic answer.

so, number of arrangements = n!/ 2! 3! = 8! / 2! 3! = 3360