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

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

 

Option: 1

40,640


Option: 2

16,600


Option: 3

26,400


Option: 4

90,720


Answers (1)

best_answer

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

The word "APPRECIATE" has a total of 11 letters, so there are 10 remaining letters to arrange (excluding the fixed P).

The 10 remaining letters can be arranged in 10! ways. However, within this arrangement, the letters P, R, and E 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 P is given by:

10 ! /(2 ! \times 2 ! \times 2 !)=(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) /(2 \times 1 \times 2 \times 1 \times 2 \times 1)=725,760 / 8=90,720

Thus, there are 90,720 ways to arrange the letters of the word "APPRECIATE" such that the first letter is P.

 

Posted by

Pankaj Sanodiya

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