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How many ways can it be arranged on a shelf?
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12 Jul 2011, 02:22
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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!)^5 D) 20! E) 5!
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Re: How many ways can it be arranged on a shelf?
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12 Jul 2011, 02:33
20!/((4!)^5) Answer  C
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Re: How many ways can it be arranged on a shelf?
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12 Jul 2011, 02:35
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!)^5 D) 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!)^m 20!/(4!)^5= C



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Re: How many ways can it be arranged on a shelf?
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30 Sep 2011, 04:47
Could someone explain me the rationale behind this formula ? Posted from GMAT ToolKit



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Re: How many ways can it be arranged on a shelf?
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30 Sep 2011, 09:31
Loki2612 wrote: Could someone explain me the rationale behind this formula ? Posted from GMAT ToolKitWe have 5 books A,B,C,D,E and 4 copies of each. Therefore we have A1,A2,A3,A4,B1,B2,B3,B4,C1,C2,C3,C4,D1,D2,D3,D4,E1,E2,E3,E4 = 20 BOOKS The way to rearrange 20 items is by 20x19x18x17x16....=20! Lets keep in mind that we rearrange our 4 copies of each book by 4x3x2x1=4! Therefore we have 5 items repeated 4 times and we need to account for the copies resulting in 20! divided by 4!x4!x4!x4!x4! Result is option C = 20!/(4!)^5



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Re: How many ways can it be arranged on a shelf?
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30 Sep 2011, 12:31
Look it as number of ways of arranging AAAA BBBB CCCC DDDD EEEE books where A,B,C,D,E repeat 4 times. hence 20!/ 4!^5



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Re: How many ways can it be arranged on a shelf?
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30 Sep 2011, 18:53
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!. AB1B2 AB2B1  duplicate as B1=B2 B1AB2 B2AB1  duplicate as B1=B2 B1B2A B2B1A  duplicate as B1=B2 so 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 ? Posted from GMAT ToolKit



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Re: How many ways can it be arranged on a shelf?
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01 Oct 2011, 04:27
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!)^5 D) 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!)^m 20!/(4!)^5= C thnx for the formula. please tell me what is the formula if order is not important
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Re: How many ways can it be arranged on a shelf?
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01 Oct 2011, 04:31
C It's a basic formula
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Re: How many ways can it be arranged on a shelf?
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06 Dec 2018, 18:11
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!)^5 D) 20! E) 5! Let A, B, C, D, and E represent the 5 different books So, 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: C Cheers, Brent
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