Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 21 Apr 2010
Posts: 10

Gordon buys 5 dolls for his 5 nieces. The gifts include two
[#permalink]
Show Tags
14 Jun 2010, 05:39
Question Stats:
60% (01:09) correct 40% (01:12) wrong based on 44 sessions
HideShow timer Statistics
Hello, a question in Manhattan GMAT guide. Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If the youngest niece doesn't want the G doll, in how many different ways can he give the gifts? My ans: Total no. of ways to give gifts = 5P5 /2! = 5!/2! = 60. How do I account for the youngest niece's condition?






Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
14 Jun 2010, 11:10




Manager
Joined: 24 Mar 2010
Posts: 92

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
14 Jun 2010, 13:40
Another way: Youngest niece needs to choose between S,S, E & T. case 1) chooses S ==> 4! ways to distribute rest of toys case 2) doesnt choose S ==> 2 ways * (distribute SSXX to 4 children) = 2 * 4!/2! = 24 Total = 24+24 = 48...
_________________
Please do consider giving kudos if you like my posts



Manager
Joined: 10 Nov 2010
Posts: 214
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

getting of a doll
[#permalink]
Show Tags
16 Feb 2011, 13:21
Pls chk the image as per my solution youngest gal can take doll from 5dolls except one.other gal can also take from rest 4 nd so on 4*4*3*2*1=96 But OA is 48
Attachments
gettting of a doll.JPG [ 29.22 KiB  Viewed 14215 times ]
_________________
The proof of understanding is the ability to explain it.



Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: getting of a doll
[#permalink]
Show Tags
16 Feb 2011, 13:43
Gordon buys 5 dolls for his 5 nieces. The gifts include 2 identical SunandFun beach dolls, one Elegant Eddie dressup doll, one G.I. Josie army doll, and one Tulip Troll doll. If the youngest niece doesn't want the G.I. Josie doll, in how many different ways can he give the gifts?5 nieces: 1  2  3  4 5 5 dolls:  S  S  E  G T 1 doesn't want G. Now if she gets E then the other four dolls (SSGT) can be assigned in 4!/2! ways (permutation of 4 letters out of which 2 S's are identical), the same if she gets T, and if gets S then the other four dolls (SEGT) can be assigned in 4! ways: 4!/2!+4!/2!+4!=48. Or total was to assign SSEGT to 5 nieces is 5!/2! and ways to assign G to 1 is 4!/2! (the same as E to 1), so desired=totalrestriction=5!/2!4!/2!=48.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
18 Feb 2011, 02:00



Retired Moderator
Joined: 16 Nov 2010
Posts: 1451
Location: United States (IN)
Concentration: Strategy, Technology

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
19 Feb 2011, 01:13
Yeah, got it now. Thanks a lot..
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 08 Nov 2010
Posts: 349
WE 1: Business Development

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
19 Feb 2011, 12:06
...and ways to assign G to 1 is 4!/2! (the same as E to 1)... Eh, i understand why its 4!/2! when its 4 dolls to 2 girls when 2 is identical. buy why its the same if u give her G? can u please explain? thanks.
_________________
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
19 Feb 2011, 12:16
144144 wrote: ...and ways to assign G to 1 is 4!/2! (the same as E to 1)...
Eh, i understand why its 4!/2! when its 4 dolls to 2 girls when 2 is identical.
buy why its the same if u give her G? can u please explain?
thanks. When you give one doll to the youngest niece you you are left with 4 dolls to assign to 4 sisters. If you give the youngest niece E, G or T then 4 dolls left will have 2 identical S's and # of ways to distribute will be 4!/2! and if you give the youngest niece S then all 4 dolls left will be distinct so # of ways to distribute them will be 4!. So what's the difference whether you give the youngest niece E or G? In both cases you distribute 4 out which 2 are identical.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 17 Feb 2011
Posts: 151
Concentration: Real Estate, Finance
Schools: MIT (Sloan)  Class of 2014

Re: MGMAT permutationsCombination
[#permalink]
Show Tags
19 Feb 2011, 13:58
After calculating 5!/2!, you can use the "reduce the pool technique" to find the number of ways in which G doll would be given to the youngest niece.



Senior Manager
Joined: 29 Jan 2011
Posts: 308

Re: getting of a doll
[#permalink]
Show Tags
08 Sep 2011, 23:06
GMATD11 wrote: Pls chk the image
as per my solution
youngest gal can take doll from 5dolls except one.other gal can also take from rest 4 nd so on
4*4*3*2*1=96
But OA is 48 I got 96 too and same way i dont understand when do we have to do 96/2!? Okay, so dolls sun and fun is similar so what? I dont get the concept of dividing by 2?? Please explain ?



Intern
Joined: 13 Jan 2012
Posts: 39

5 Dolls for 5 nieces
[#permalink]
Show Tags
30 Jan 2012, 21:50
Gordon buys 5 dolls for his 5 nieces. The gifts include 2 identical "S" dolls, one "E" doll, one "J" doll and one "T" doll. If the youngest niece does not want the "J" doll, in how many different ways can he give the gifts?
Response:
Strategy: 1) Calculate TOTAL number of ways the 5 dolls  S, S, E, J, T  can be assigned to 5 people. 2) Keeping the fifth doll constant ("J"), Calculate TOTAL number of ways that the 4 dolls  S, S, E, T  can be assigned to 4 people. 3) Subtract (2) from (1)
Calculations: 1) 5!/2! = 60 2) 4!/2! = 12 3) 6012 = 48
Does this seem right? Any other way that you'd approach this?
Book's Response (scroll below)... . . . . . . 48



Intern
Joined: 04 Mar 2011
Posts: 18

Re: 5 Dolls for 5 nieces
[#permalink]
Show Tags
30 Jan 2012, 22:00
looks right to me. find total possibility 5!/2! = 60 subtract the chances of of the youngest getting the doll she doesnt want 4!/2! and you get 48 so yea looks right to me. good job.
That should be the only way you approach the problem



Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: 5 Dolls for 5 nieces
[#permalink]
Show Tags
31 Jan 2012, 01:10
Merging similar topics. fxsunny wrote: Gordon buys 5 dolls for his 5 nieces. The gifts include 2 identical "S" dolls, one "E" doll, one "J" doll and one "T" doll. If the youngest niece does not want the "J" doll, in how many different ways can he give the gifts?
Response:
Strategy: 1) Calculate TOTAL number of ways the 5 dolls  S, S, E, J, T  can be assigned to 5 people. 2) Keeping the fifth doll constant ("J"), Calculate TOTAL number of ways that the 4 dolls  S, S, E, T  can be assigned to 4 people. 3) Subtract (2) from (1)
Calculations: 1) 5!/2! = 60 2) 4!/2! = 12 3) 6012 = 48
Does this seem right? Any other way that you'd approach this?
Book's Response (scroll below)... . . . . . . 48 Your solution is correct.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 07 Nov 2011
Posts: 21

Re: 5 Dolls for 5 nieces
[#permalink]
Show Tags
08 Feb 2012, 11:12
hi bunnuel,
You are explaining the same method again and again. Can u please explain the slot method for this question . From that i too get the answer as 96 4*4*3*2*1



Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: 5 Dolls for 5 nieces
[#permalink]
Show Tags
08 Feb 2012, 11:26



Intern
Joined: 07 Nov 2011
Posts: 21

Re: 5 Dolls for 5 nieces
[#permalink]
Show Tags
08 Feb 2012, 19:51
Bunuel wrote: vaibhav123 wrote: hi bunnuel,
You are explaining the same method again and again. Can u please explain the slot method for this question . From that i too get the answer as 96 4*4*3*2*1 Correct answer is 48, not 96. Please, explain your logic behind your answer and Ill try to point out the flaw in it. for the niece who does not want a particular type can be assigned a doll in 4 ways .since 1 doll is assigned out of 5 .Now 4 reminingn can be assigned to other 4 and then 3 to other 3 , then 2 to other 2 and then 1 4*4*3*2*1 I dont get the logic behind when to divide by 2 or not since if 5 same rings are to be distributed in five fingers, we use the slot method llike this 5*4*3*2*1 and we dont divide it by 5(in this case also 5 rings are identical), so in the above question why we have to divide it by 2.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India

Re: 5 Dolls for 5 nieces
[#permalink]
Show Tags
09 Feb 2012, 01:43
vaibhav123 wrote: Bunuel wrote: vaibhav123 wrote: hi bunnuel,
You are explaining the same method again and again. Can u please explain the slot method for this question . From that i too get the answer as 96 4*4*3*2*1 Correct answer is 48, not 96. Please, explain your logic behind your answer and Ill try to point out the flaw in it. for the niece who does not want a particular type can be assigned a doll in 4 ways .since 1 doll is assigned out of 5 .Now 4 reminingn can be assigned to other 4 and then 3 to other 3 , then 2 to other 2 and then 1 4*4*3*2*1 I dont get the logic behind when to divide by 2 or not since if 5 same rings are to be distributed in five fingers, we use the slot method llike this 5*4*3*2*1 and we dont divide it by 5(in this case also 5 rings are identical), so in the above question why we have to divide it by 2. Note here that the youngest niece can be assigned a doll in only 3 ways: One of the S dolls (they are both identical so it doesn't matter which one she gets) or E doll or T doll How you would assign the rest of the dolls would depend on which doll the youngest one got. If she got an S doll, you can assign a doll to the next niece in 4 ways: S or E or G or T. If she got, say, the E doll, you assign a doll to the next niece in 3 ways: S or G or T. This complicates this method. Instead, try and assign nieces to the dolls since all nieces are distinct. G doll can be assigned a niece in 4 ways (the youngest doesn't want her) E doll can be assigned a niece in 4 ways again (the remaining 4 after one niece has been assigned to G doll) T doll can be assigned a niece in 3 ways (remaining 3 nieces) Now we have 2 identical dolls and 2 nieces. How will you assign them? You will give the nieces 1 doll each. There is no other way. Both dolls are same so it doesn't matter who gets which one. Total number of allocations = 4*4*3 = 48 (or use one of the other great methods discussed above)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 10 Jan 2010
Posts: 159
Location: Germany
Concentration: Strategy, General Management
GPA: 3
WE: Consulting (Telecommunications)

Re: Gordon buys 5 dolls for his 5 nieces. The gifts include two
[#permalink]
Show Tags
09 Feb 2012, 02:05
Total number of ways 5C2 = 60 (as on gift is the same) One does not want to have one specific gift item (Number of ways the niece can get this item) = 4C2 = 12
Total ways to provide gifts = 48 ways



Intern
Joined: 28 Dec 2010
Posts: 19

Re: Gordon buys 5 dolls for his 5 nieces. The gifts include two
[#permalink]
Show Tags
20 Feb 2012, 02:41
Hi Bunel , To your first post : Total # of ways to distribute SSEGT among 5 sisters (without restriction) is !5/!2 =60 ;I am trying to understand how did you came to this !5/!2 ?
Is it a permutation of picking 5 out of 5 where 2 are same  5P2/!2 ? If this is correct so can it be like if there were 3 sisters instead of 5 , with all other condition intact ,the solution would have been 
Total # of ways to distribute SSEGT among 3 sisters (without restriction) is 5P3/!2 = 15; The # of ways when the youngest niece gets G is: 4P2/!2 = 6 (give G to youngest and then distribute SSET among 2 sisters).
So, # of ways when youngest niece doesn't get G is:156 = 9 .
Please explain for better understanding . Thanks.




Re: Gordon buys 5 dolls for his 5 nieces. The gifts include two &nbs
[#permalink]
20 Feb 2012, 02:41



Go to page
1 2
Next
[ 29 posts ]



