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  • In how many ways can the letters of the word "ENGINEER" be arranged such that the word should have the first letter I?  Option: 1</stron

In how many ways can the letters of the word "ENGINEER" be arranged such that the word should have the first letter I?

 

Option: 1

1460


Option: 2

1660


Option: 3

1440


Option: 4

1260


Answers (1)

best_answer

To calculate the number of ways the letters of the word "ENGINEER" can be arranged such that the first letter is I, we can fix the first letter as I and then arrange the remaining letters.

The word "ENGINEER" has a total of 8 letters, so there are 7 remaining letters to arrange (excluding the fixed I).

The 7 remaining letters can be arranged in 7! ways. However, within this arrangement, the letters E and R each repeat twice. Therefore, we need to divide by 2! for each repeated letter.

Therefore, the total number of arrangements where the first letter is I is given by:

7 ! /(2 ! \times 2 !)=(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) /(2 \times 1 \times 2 \times 1)=5,040 / 4=1,260.

Thus, there are 1,260 ways to arrange the letters of the word "ENGINEER" such that the first letter is I.

 

Posted by

rishi.raj

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