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

 It is currently 06 Jul 2015, 10:13

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Current Student
Joined: 31 Aug 2007
Posts: 371
Followers: 1

Kudos [?]: 63 [0], given: 1

how many ways can you place 9 marbles in 3 hats so that a) [#permalink]  04 May 2008, 07:26
00:00

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
Joined: 10 Jun 2007
Posts: 1463
Followers: 6

Kudos [?]: 143 [0], given: 0

Re: PS groups [#permalink]  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
Joined: 31 Aug 2007
Posts: 371
Followers: 1

Kudos [?]: 63 [0], given: 1

Re: PS groups [#permalink]  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 Replies Last post
Similar
Topics:
9 How many ways can 5 different colored marbles be placed in 3 2 14 Oct 2013, 07:53
12 How many ways are there of placing 6 marbles in 4 bowls 11 12 Aug 2012, 12:21
From a list of 1-8, how many ways can you pick 3 numbers so 7 20 Aug 2007, 12:25
Display posts from previous: Sort by