How many ten letter words can be formed with all the letters of the word ‘ENGAGEMENT’?Choices:- 10! 10! / (3! x 2! x 2!) 10! / (3! x 2!) 10! / 3

The word 'ENGAGEMENT' has 10 letters in total. However, some letters are repeated. The letter 'E' is repeated 3 times, 'N' is repeated 2 times, and 'G' is repeated 2 times.

When forming words with these letters, we need to account for the fact that swapping two 'E's, two 'N's, or two 'G's doesn't create a new word.

The total number of ways to arrange 10 items is 10 factorial (10!).

However, we need to divide this by the number of ways to arrange the 3 'E's, the 2 'N's, and the 2 'G's. This is 3 factorial (3!) for the 'E's, 2 factorial (2!) for the 'N's, and 2 factorial (2!) for the 'G's.

So, the total number of ten letter words that can be formed with all the letters of the word ‘ENGAGEMENT’ is 10! / (3! x 2! x 2!).

Therefore, the correct choice is 10! / (3! x 2! x 2!).