Final answer:
To find the number of different words that can be made with the letters of the word 'nainital' such that each word begins with 'l' and ends with 't', we remove the first and last letters, calculate the arrangements of the remaining letters, and account for repeated letters.
Step-by-step explanation:
To find the number of different words that can be made with the letters of the word 'nainital' such that each word begins with 'l' and ends with 't', we first need to determine the number of arrangements of the remaining letters. The word 'nainital' has 8 letters in total, including the 'l' and 't'. Removing the first and last letters, we are left with 'ainita'. There are 6 factorial (6!) ways to arrange these letters.
Next, we need to consider the repetition of 'a' and 'i' in the letters. There are 2 'a's and 2 'i's, so we divide the total number of arrangements by (2!)(2!) to account for the repeated letters.
Therefore, the number of different words that can be made is given by:
(6!) / (2!)(2!) = 360 / 4 = 90 different words.