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

Question

Quizplus · Accepted Answer

The word DISAPPOINT has 10 letters in total, with the letter P repeated twice. The total number of arrangements can be calculated using the formula for permutations of a multiset: $n! / (n_1! \cdot n_2! \cdot \ldots \cdot n_k!)$, where $n$ is the total number of items to arrange, and $n_1, n_2, \ldots, n_k$ are the counts of each repeated item. Here, $n = 10$ and $n_1 = 2$ (for the two Ps), so the total number of arrangements is $10! / 2! = 3,628,800 / 2 = 1,814,400 / 2 = 907,200$.

How Many Arrangement Are There of the Letters DISAPPOINT