Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together?Option: 1 20,640

How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together?

Option: 1

20,640


Option: 2

56,600


Option: 3

66,400


Option: 4

37,800


Answers (1)

best_answer

To calculate the number of ways the letters of the word "ARRANGE" can be arranged such that the two R's are never together, we can consider treating the two R's as distinct entities (R1 and R2).

The word "ARRANGE" has a total of 7 letters, but since the two R's are treated as distinct entities, we have a total of 8 entities to arrange (A, R1, R2, A, N, G, E).

We can arrange these 8 entities in 8! ways. However, within this arrangement, we need to consider the cases where the two R's are together.

To calculate the number of arrangements where the two R's are together, we can treat the two R's as a single entity. Then we have 7 entities to arrange (A, (R1R2), A, N, G, E). We can arrange these 7 entities 7! in ways. However, within this arrangement, the two A's repeat, so we need to divide by 2!

Therefore, the number of arrangements where the two R's are together is (7! / 2!).

To calculate the number of arrangements where the two R's are not together, we subtract the number of arrangements where the two R's are together from the total number of arrangements:

Total arrangements - Arrangements with R's together = 8 !-(7 ! / 2 !)
=40320-(5040 / 2)
=40320-2520
=37800

Therefore, there are 37800 ways to arrange the letters of the word "ARRANGE" such that the two R's are never together.

 

Posted by

mansi

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

75% criteria for JEE Main 2025 not removed; eligibility criteria for admission to IITs
anam-khan

BTech Admissions 2025 LIVE: AEEE phase 1 exam date out, JEE Mains registration ongoing; BITSAT, VITEEE updates
anam-khan

JEE Main 2025 Eligibility Criteria: What is state code of eligibility? Here’s list of qualifying exams

Latest Question