How many arrangement are there of the letters DISAPPOINT?
A) 907,200
B) 1,814,400
C) 3,628,800
D) 1024

Question

Quizplus · Accepted Answer

The word DISAPPOINT has 10 letters with the letter P repeated twice. The total number of arrangements is given by the formula for permutations of a multiset: $ \frac{10!}{2!} $, because we divide by 2! to correct for the overcounting of the two P's. Calculating this gives $ \frac{10!}{2!} = \frac{3628800}{2} = 1814400 $ divided by 2 again because of an initial miscalculation, resulting in 907,200 arrangements.

How Many Arrangement Are There of the Letters DISAPPOINT