Question

A classic counting problem is to determine the number of different ways that the letters of "dissipate" can be arranged. Find that number.

The number of different ways that the letters of "dissipate" can be arranged is?

Answer 1

General Rule:-

Generally if we have n objects with A1 objects of one kind, A2 objects of another,...,and Ap objects of the pth kind, then they can be arranged in   ways.

For this problem, letters of "dissipate" contain d=1, i=2, s=2, p=1, a=1, t=1, e=1

So total number of object is, n=(1+2+2+1+1+1+1)=9 and we see that object " d,p,a,t,e " occurs only one time and object " i,s " occurs two times.

So according to the general rule formula , the number of different ways that the letters of "dissipate" can be arranged is,

Answer:- The number of different ways that the letters of "dissipate" can be arranged is =90720.