Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Oct 2014, 07:28

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

how many ways can you place 9 marbles in 3 hats so that a)

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Current Student
User avatar
Joined: 31 Aug 2007
Posts: 370
Followers: 1

Kudos [?]: 41 [0], given: 1

how many ways can you place 9 marbles in 3 hats so that a) [#permalink] New post 04 May 2008, 07:26
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
how many ways can you place 9 marbles in 3 hats so that a) each hat has at least 1 marble b) a hat may not have any marbles.
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 6

Kudos [?]: 108 [0], given: 0

Re: PS groups [#permalink] New post 05 May 2008, 12:47
young_gun wrote:
how many ways can you place 9 marbles in 3 hats so that a) each hat has at least 1 marble b) a hat may not have any marbles.


I'll take a shot...

You have 9 marbles total, and all marbles are exactly the same.
You want at least one marble in each hat...so let's work it out.

Say you have Hat (A, B, C)
If hat A gets 1 marble, you have
(1, 1, 7)
(1, 2, 6)
(1, 3, 5)
(1, 4, 4)
(1, 5, 3)
(1, 6, 2)
(1, 7, 1)
Total of 7

If hat B gets 2, you have
(2, 1, 6)
(2, 2, 5)
(2, 3, 4)
(2, 4, 3)
(2, 5, 2)
(2, 6, 1)
Total of 6

If you see the pattern, you have...
If A=1, Total = 7 ways
If A=2, Total = 6 ways
If A=3, Total = 5 ways
...
If A=7, Total = 1 way
You know that A cannot be more than 7 because other hats will not get any marbles. So number of marbles in A stops at 7. Now add up the total to get the answer for (a)...
7+6+5+4+3+2+1 = 28 ways


For (b), you have hat A with 0 marbles, do the same thing, you get
(0, 1, 8)
...
(0, 8, 1)
Total of 8
Do the same if hat B has 0 and hat C has 0 marbles, you get a total of
8*3 = 24 ways
Current Student
User avatar
Joined: 31 Aug 2007
Posts: 370
Followers: 1

Kudos [?]: 41 [0], given: 1

Re: PS groups [#permalink] New post 05 May 2008, 16:43
bkk145 wrote:
young_gun wrote:
how many ways can you place 9 marbles in 3 hats so that a) each hat has at least 1 marble b) a hat may not have any marbles.


I'll take a shot...

You have 9 marbles total, and all marbles are exactly the same.
You want at least one marble in each hat...so let's work it out.

Say you have Hat (A, B, C)
If hat A gets 1 marble, you have
(1, 1, 7)
(1, 2, 6)
(1, 3, 5)
(1, 4, 4)
(1, 5, 3)
(1, 6, 2)
(1, 7, 1)
Total of 7

If hat B gets 2, you have
(2, 1, 6)
(2, 2, 5)
(2, 3, 4)
(2, 4, 3)
(2, 5, 2)
(2, 6, 1)
Total of 6

If you see the pattern, you have...
If A=1, Total = 7 ways
If A=2, Total = 6 ways
If A=3, Total = 5 ways
...
If A=7, Total = 1 way
You know that A cannot be more than 7 because other hats will not get any marbles. So number of marbles in A stops at 7. Now add up the total to get the answer for (a)...
7+6+5+4+3+2+1 = 28 ways


For (b), you have hat A with 0 marbles, do the same thing, you get
(0, 1, 8)
...
(0, 8, 1)
Total of 8
Do the same if hat B has 0 and hat C has 0 marbles, you get a total of
8*3 = 24 ways



thanks for your response...in asking that question, i was hoping to find out whether there is a short-cut way to determine the number of ways you could split X objects amongst Y containers. I think I have seen a really elegant solution to such a problem on this forum however I cant seem to find it now...
Re: PS groups   [#permalink] 05 May 2008, 16:43
    Similar topics Author Replies Last post
Similar
Topics:
8 How many ways can 5 different colored marbles be placed in 3 praffulpatel 2 14 Oct 2013, 07:53
How many ways can you distribute 5 marbles in 3 identical ba alphabeta1234 0 30 Aug 2013, 16:42
How many ways can you distribute 5 marbles in 3 baskets hairen 0 16 Jun 2013, 06:01
12 Experts publish their posts in the topic How many ways are there of placing 6 marbles in 4 bowls Galiya 11 12 Aug 2012, 12:21
From a list of 1-8, how many ways can you pick 3 numbers so misterJJ2u 7 20 Aug 2007, 12:25
Display posts from previous: Sort by

how many ways can you place 9 marbles in 3 hats so that a)

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.