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  • How many different 7-letter words can be formed using the letters of the word "EXAMPLE"?Option: 1 3096<div class='q

How many different 7-letter words can be formed using the letters of the word "EXAMPLE"?

Option: 1

3096


Option: 2

5040


Option: 3

4196


Option: 4

6020


Answers (1)

best_answer

To determine the number of different 7-letter words that can be formed using the letters of the word "EXAMPLE," we can use the concept of permutations.

The word "EXAMPLE" has a total of 7 letters. We need to choose 7 letters from these 7 letters to form a 7-letter word without repetition.

The number of ways to arrange 7 letters out of 7 without repetition can be calculated as the permutation of 7 letters taken 7 at a time is given by,

\begin{aligned} { }^7 P_7 & =\frac{7 !}{(7-7) !} \\ { }^7 P_7 & =7 \times 6 \times 5 \times 4 \times 3 \times 2 \\ { }^7 P_7 & =5040 \end{aligned}

Therefore, the number of words formed is 5040.

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Gaurav

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