Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now
 Manager Joined: 29 Jun 2010 Posts: 217 Schools:LBS, Oxford
How many ways can it be arranged on a shelf? [#permalink]
00:00
Difficulty:
Question Stats: Hide Show timer StatisticsThere are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?A) 20!/4!B) 20!/5(4!)C) 20!/(4!)^5D) 20! E) 5!
Re: How many ways can it be arranged on a shelf? [#permalink]
Alchemist1320 wrote: There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?A) 20!/4!B) 20!/5(4!)C) 20!/(4!)^5D) 20! E) 5! Let A, B, C, D, and E represent the 5 different booksSo, we want to arrange the following 20 letters: AAAABBBBCCCCDDDDEEEE-------ASIDE---------------------------------------------When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....] So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:There are 11 letters in total There are 4 identical I's There are 4 identical S's There are 2 identical P's So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]----------ONTO THE QUESTION--------------------------GIVEN: AAAABBBBCCCCDDDDEEEE There are 20 letters in total There are 4 identical A's There are 4 identical B's There are 4 identical C's There are 4 identical D's There are 4 identical E's So, the total number of possible arrangements = 20!/[(4!)(4!)(4!)(4!)(4!)] = 20!/[(4!)^5]Answer: CCheers,Brent _________________
Brent Hanneson – Creator of gmatprepnow.comI’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is… Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Retired Moderator Joined: 16 Nov 2010 Posts: 996 Location: United States (IN) Concentration: Strategy, Technology
Re: How many ways can it be arranged on a shelf? [#permalink] 20!/((4!)^5)Answer - C _________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings
Current Student Joined: 26 May 2005 Posts: 381
Re: How many ways can it be arranged on a shelf? [#permalink]
Alchemist1320 wrote: There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?A) 20!/4!B) 20!/5(4!)C) 20!/(4!)^5D) 20! E) 5! formula : The number of ways in which MN different items can be divided equally into M groups, each containing N objects and the order of the groups is important is = (mn)!/(n!)^m20!/(4!)^5= C
Intern Joined: 09 Aug 2011 Posts: 18 Concentration: Entrepreneurship Schools: Insead '13 (A)
Re: How many ways can it be arranged on a shelf? [#permalink] Could someone explain me the rationale behind this formula ?
Re: How many ways can it be arranged on a shelf? [#permalink]
Loki2612 wrote: Could someone explain me the rationale behind this formula ? Result is option C = 20!/(4!)^5
Intern Joined: 25 Dec 2010 Posts: 43
Re: How many ways can it be arranged on a shelf? [#permalink] Look it as number of ways of arranging AAAA BBBB CCCC DDDD EEEE books where A,B,C,D,E repeat 4 times.
Senior Manager Joined: 01 Feb 2011 Posts: 379
Re: How many ways can it be arranged on a shelf? [#permalink] 20! / ((4!)^5)this division is done to avoid repetitions.Lets say we have to figure out number of arrangements for A,B1,B2. (where B1=B2) . total arrangements for 3 letters is 3!.A-B1-B2A-B2-B1 - duplicate as B1=B2B1-A-B2B2-A-B1 - duplicate as B1=B2B1-B2-AB2-B1-A - duplicate as B1=B2so to avoid duplicates we need to divide the total arrangements/ (number of similar items)! = 3!/2! Loki2612 wrote: Could someone explain me the rationale behind this formula ?
Current Student Joined: 23 Oct 2010 Posts: 279 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A)
Re: How many ways can it be arranged on a shelf? [#permalink]
sudhir18n wrote: Alchemist1320 wrote: There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?A) 20!/4!B) 20!/5(4!)C) 20!/(4!)^5D) 20! E) 5! 20!/(4!)^5= C thnx for the formula. please tell me what is the formula if order is not important _________________
Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth
Manager Joined: 20 Aug 2011 Posts: 69
Re: How many ways can it be arranged on a shelf? [#permalink]
Non-Human User Joined: 09 Sep 2013 Posts: 25244
Re: How many ways can it be arranged on a shelf? [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: How many ways can it be arranged on a shelf? [#permalink] 11 Jul 2022, 02:18 |
There are 6 copies each of 3 different books in how many ways can they be arranged on a shelf
Pos Terkait
Copyright © 2024 ketajaman Inc.
