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  • In how many ways can the letters of the word "PERMUTE" be arranged if all the letters must be used?Option: 1 126

In how many ways can the letters of the word "PERMUTE" be arranged if all the letters must be used?

Option: 1

1260


Option: 2

9630


Option: 3

7850


Option: 4

3350


Answers (1)

best_answer

To find the number of ways the letters of the word "PERMUTE" can be arranged if all the letters must be used, we can consider it as a permutation problem.

The word "PERMUTE" consists of 7 letters. Let's break down the calculation step by step:

Calculate the total number of arrangements without any restrictions:

The word has 7 letters, so there are 7 possible positions for the first letter, 6 remaining positions for the second letter, 5 for the third, and so on, until 1 position for the last letter. This can be expressed as

Adjust for the repeated letters:

In the word "PERMUTE," both the letter 'E' and 'P' appear twice. To avoid overcounting, we need to divide the total number of arrangements by the factorial of the number of repeated letters. In this case, we divide by for the two 'E's and another for the two 'P's.

Therefore, the adjusted calculation is: 7!/(2!\times2!)

Simplify the expression:

Evaluating the factorial expressions:

7!=5040

2!=2

Substituting these values into the adjusted calculation:

5040 /(2 \times 2)=5040 / 4=1260

Therefore, there are 1260 ways to arrange the letters of the word "PERMUTE" if all the letters must be used.

Hence option 1 is correct.

 

 

 

 

Posted by

avinash.dongre

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