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' appears 3 times, 'N' appears 2 times, and 'G' appears 2 times.

When forming words with these letters, the repeated letters can be arranged in fewer ways than the unique letters.

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

However, we must divide this by the number of ways to arrange the repeated letters.

The number of ways to arrange 3 'E's is 3 factorial (3!). The number of ways to arrange 2 'N's is 2 factorial (2!). The number of ways to arrange 2 'G's is 2 factorial (2!).

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!).