How many different words can be formed using the letters of the words “EXAMINATION‘?

To solve this problem, we need to use the formula for permutations of a multiset. This formula is n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of item.

Step 1: Count the total number of letters in the word "EXAMINATION". There are 11 letters.

Step 2: Count the number of times each letter appears. E appears 1 time, X appears 1 time, A appears 2 times, M appears 1 time, I appears 2 times, N appears 2 times, T appears 1 time, O appears 1 time.

Step 3: Substitute these values into the formula. The number of different words is 11! / (1! * 1! * 2! * 1! * 2! * 2! * 1! * 1!) = 39,916,800.

So, 39,916,800 different words can be formed using the letters of the word "EXAMINATION".