How many different strings can be formed by rearranging the letters in the word troposphere?

Step-by-step explanation:

The letters of the word troposphere can be sorted to be:

ee h oo pp rr s t

with 7 distinct letters of which 4 are in pairs for a total of 11 letters.

The number of words that can be formed from n distinct letters

= n! / (1!1!1! ... 1!) [n times in the denominator]

The number of words that can be formed from n letters of which 2 are duplicated and the rest distinct is

= n! / (2!1!1! ... 1!) [n-1 times 1!]

Similarly, the number of words that can be formed from 11 letters, of which there are 4 pairs of duplicated letters is

N=11! / (2!2!2!2!1!1!1!)

= 39916800 / (2*2*2*2*1*1*1)

= 2494800