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!
Question
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!
Solution
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, these repeated letters can be arranged in the same position, creating identical words. To avoid counting these as separate words, we divide by the factorial of the number of times each letter is repeated.
So, the number of ten letter words that can be formed with all the letters of the word ‘ENGAGEMENT’ is given by the formula:
10! / (3! x 2! x 2!)
So, the correct choice is 10! / (3! x 2! x 2!).
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