UrbanPro

Location Set your Location

Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > In how many ways can the letters of the PERMUTATIONS...
✕

Search in

In how many ways can the letters of the PERMUTATIONS be arranged if there are always 4 letters between P and S ?

Asked by Last Modified  

6 Answers

Learn Class XI-XII Tuition (PUC)

Follow 0
Answer

Please enter your answer

Tutor

I figured out the solution however it is not a simple permutation question. This includes both permutation as well as combination. There are 12 words in letter PERMUTATIONS. Out of which T is repeated twice. Now first we need to see how many ways we can make word with 4 letter between P and S. Except...
read more
I figured out the solution however it is not a simple permutation question. This includes both permutation as well as combination. There are 12 words in letter PERMUTATIONS. Out of which T is repeated twice. Now first we need to see how many ways we can make word with 4 letter between P and S. Except P and S there are total of 10 letters, so number of way of selecting them = 10C4 = 210 Also note that question is asking to place exactly 4 words between P and S, but does not tells you if P has to be the first letter of S has to be the first letter. So In all the above combinations, we can rotate the position of P and S. So total way = 210*2 = 420 The selected 4 letters can be rotated between P and S in = 4! ways So total ways = 420 * 4! Consider this 6 letter chunk (P, S, and 4 letter between them) as 1 letter. Remaining letters are 6. So in total we have 7 letters, which can be arranged in 7! ways. So total number of ways = 7! * 420 * 4! Now since letter T was repeated twice, we should divide the above result by 2!. So Total number of ways = 7! * 420 * 4! / 2! = 25401600 read less
Comments
Dislike Bookmark

Tutor

This is a 12 letter word. Let each position of the word be numbered. So there are 12 positions to fill in. _ _ _ _ _ _ _ _ _ _ _ _ if P is in position 1 then 'S' will be in number 6, position 2,3,4,5 will be occupied by some other four letters. Let us call this pair (1,6) Similarly for position...
read more
This is a 12 letter word. Let each position of the word be numbered. So there are 12 positions to fill in. _ _ _ _ _ _ _ _ _ _ _ _ if P is in position 1 then 'S' will be in number 6, position 2,3,4,5 will be occupied by some other four letters. Let us call this pair (1,6) Similarly for position of 'P' at 2 ,3 4, 5 ,6 and 7. This gives 7 cases. If we reverse order between p and s we get another 7 cases Total 14 cases. Leaving out p and s there are 10 letters with t coming twice. These can take any of those 10 places left out by gaps in 10!/2! ways. So total 14* 10!/2! = 7 * 10*9*8*7*6*5*4*3*2 = 25401600 read less
Comments
Dislike Bookmark

GMAT Math Expert

Ans: 7*2!*(10!/2!) = 7*10! P _ _ _ _ S _ _ _ _ _ _(One way to place P and S P and S can be arranged with a 4 letter difference in between them in 7*2! ways. Remaining 10 letters (E R M U A I O N TT) can be arranged in 10!/2! ways.
Comments
Dislike Bookmark

Tutor - Maths and computer science

There are 12 letters in the word "PERMUTATIONS", out of which T is repeated twice. 1. Choosing 4 letters out of 10 (12-2(P and S)=10) to place between P and S = 10C4 = 210; 2. Permutation of the letters P ans S (PXXXXS or SXXXXP) = 2! =2; 3. Permutation of the 4 letters between P and S = 4! =24; 4....
read more
There are 12 letters in the word "PERMUTATIONS", out of which T is repeated twice. 1. Choosing 4 letters out of 10 (12-2(P and S)=10) to place between P and S = 10C4 = 210; 2. Permutation of the letters P ans S (PXXXXS or SXXXXP) = 2! =2; 3. Permutation of the 4 letters between P and S = 4! =24; 4. Permutations of the 7 units {P(S)XXXXS(P)}{X}{X}{X}{X}{X}{X} = 7! = 5040; 5. We should divide multiplication of the above 4 numbers by 2! as there is repeated T. Hence: (10c4 x 2! x 4! x 7!) / 2! = 25,401,600 read less
Comments
Dislike Bookmark

Spoken English, BTech Tuition, C Language, C++ Language, CAD etc., with 4 years of experience

( 7! * 420 * 4! )/ 2 = 25401600
Comments
Dislike Bookmark

Don't want to over express myself, just join and feel the experience.

In the 12 letter word there are 14 different places where P and S can be separated by 4 letters. Now the remaining 10 letters can be arranged in 10!/2! ways as T repeats two times . So total no. of ways arrangement with the given condition is 14*10!/2! = 25401600
Comments
Dislike Bookmark

View 4 more Answers

Related Questions

Somebody pls explain me about the formative assessment and summative assessment followed by CBSE (for 10th class Maths .)
its just like semester system. 1 sem 1 syllabus 1 exam and aggregate of all exams will be the total %
Dhanalakshmi N.
7th term of an A.P. is 40. then find the sum of first 13 terms ?
7th term =40=a + 6d sum of 13 term =(13/2)(2a+12d)=13(a+6d)=13*40=520
Kumar Upendra Akshay
Why do the street lights and head lights of vehicles look like stars when viewed through glass ?
Refraction and diffraction plays the role
Brigade Institute
0 0
6
what is meant by relativity motion
It must be a relative motion than relativity motion. When two bodies are moving with some velocity then study of motion of one body with respect to the other body is known as relative motion. :-)
Venkata
When fast moving electrons are stopped by a metal of high atomic weight the phenomenon gives rise to __________. (X-rays, b-rays, g-rays)
X-rays
Narendra Kumar
0 0
6

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Recommended Articles

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Radhe Shyam Burman, an MBA Tutor from...

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Meet Sandhya R, a B.Sc tutor from Bangalore

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

Read full article >

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Hyderabad
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Chennai
Class 12 Tuition in Pune
Class 12 Tuition in Jaipur
Class 12 Tuition in Lucknow
Class 12 Tuition in Noida

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2024All Rights Reserved