How many words can be formed with the letters of the word 'POSTMAN', if every word begins with T and ends with M?

Concept:

If an object X can be chosen in 'a' ways and another object Y can be chosen in 'b' ways then the object X and Y can be chosen in 'ab' ways.

Calculation:

Here, there are 7 letters in the word "POSTMAN".

If we fix the first letter as T and the last letter as M then the arrangement would be like:

"T _ _ _ _ _ M"

Now we are left with 5 more letters.

The first blank space can be filled in 5 different ways by using any of the remaining letters. 

The second space can be filled in 4 different ways as one of the letters is already used to fill the first space.

Similarly, the third space can be filled in 3 different ways, the fourth in 2 different ways, and the last blank can only be filled with 1 way.

∴ Total number of ways in which we can arrange the letters = 5 × 4 × 3 × 2 × 1 = 120

Hence, the required answer is 120.