Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • 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

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Maths 2025: Five tips to score high marks in ‘toughest’ subject; most important chapters
anam-khan

JEE Main 2025 exam city intimation slip for session 1 soon at jeemain.nta.nic.in
anam-khan

Focus on modern physics, formulas to solve tricky problems; 5 tips to tackle JEE Main physics 2025

Latest Question