It is currently 15 Dec 2017, 19:40

### 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

# There are 3 candidates and 5 voters. In how many ways can

Author Message
Director
Joined: 03 Jul 2003
Posts: 651

Kudos [?]: 107 [0], given: 0

There are 3 candidates and 5 voters. In how many ways can [#permalink]

### Show Tags

06 Jan 2004, 14:18
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

There are 3 candidates and 5 voters. In how many ways can the votes be given? If 3 candidates are included in 5 voters and they vote for themselves only, then how many ways of giving votes are possible?

Ans with explanation ?

Kudos [?]: 107 [0], given: 0

Director
Joined: 28 Oct 2003
Posts: 501

Kudos [?]: 36 [0], given: 0

Location: 55405

### Show Tags

06 Jan 2004, 14:31
Quote:
In how many ways can the votes be given?

does the identity of the vote matter?

In other words, say Bob got one vote-- does it matter if the vote Bob got was from Fran or Sally?

Kudos [?]: 36 [0], given: 0

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4284

Kudos [?]: 544 [0], given: 0

### Show Tags

06 Jan 2004, 14:33
1- 3 * 5 = 15
2- 2 (voters left) * 3 = 6
_________________

Best Regards,

Paul

Kudos [?]: 544 [0], given: 0

Director
Joined: 03 Jul 2003
Posts: 651

Kudos [?]: 107 [0], given: 0

### Show Tags

06 Jan 2004, 14:36
I got this from another web site. So, I don't know the interpretation of
the question!

Kudos [?]: 107 [0], given: 0

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4284

Kudos [?]: 544 [0], given: 0

### Show Tags

06 Jan 2004, 15:06
I don't know if you need this kpadma but here it is
Let's call voters ( A B C D E )
Let's call candidates ( 1 2 3 )

Question 1: Voter A can vote for 3 diff. candidates. So you have 3 possibilities. All other candidates can also vote for 3 diff. candidates. Therefore 3*5 = 15

Question 2: Each candidates will vote for themselves, therefore, there will only be 2 voters left. Let's call those left A and B ( C D E being the candidates who voted for themselves already ). A and B can each choose 3 candidates to vote fore. Thus 2*3 = 6
_________________

Best Regards,

Paul

Kudos [?]: 544 [0], given: 0

Director
Joined: 14 Oct 2003
Posts: 582

Kudos [?]: 59 [0], given: 0

Location: On Vacation at My Crawford, Texas Ranch

### Show Tags

06 Jan 2004, 15:52
There are 3 candidates and 5 voters. In how many ways can the votes be given? If 3 candidates are included in 5 voters and they vote for themselves only, then how many ways of giving votes are possible?

Ans with explanation ?

maybe i'm not getting something here but I got something really different.

this is how i interpreted the question:

how many ways can 5 voters vote for 3 candidates?

Candidates X Y Z

X can get (6, 5, 4, 3, 2, 1*(himself-but i don't think this matters)

Thus

All 5 voters voting for Candidate X = 5C5

4 of 5 voters voting for candidate x =5C4

3 of 5 voters ditto = 5C3

2 of 5 voters ditto = 5C2

1 of 5 voters ditto = 5C1

= (1*5*10*10*5)*3 (could be x,y, or z) = 7,500 ways

i may be completely wrong.

Kudos [?]: 59 [0], given: 0

CEO
Joined: 15 Aug 2003
Posts: 3452

Kudos [?]: 928 [0], given: 781

### Show Tags

07 Jan 2004, 03:30
There are 3 candidates and 5 voters. In how many ways can the votes be given?
Ans with explanation ?

i smell permutations!

5 0 0..... 3 ways ( since 0 is not unique )
4 1 0..... 6 ways ( 3! ways)
3 1 1..... 6 ways
2 2 1. ... 6 ways

Number of ways = 21 ways

Quote:
If 3 candidates are included in 5 voters and they vote for themselves only, then how many ways of giving votes are possible?

3 candidates are included in 5 voters.

we got 2 voters and find out how many ways votes can be given to 3 candidates ( the other 3 votes have been assigned)

2 0 0 .... 3 ways
1 1 0 .... 6 ways

Total 9 ways

Kudos [?]: 928 [0], given: 781

Director
Joined: 03 Jul 2003
Posts: 651

Kudos [?]: 107 [0], given: 0

### Show Tags

09 Jan 2004, 12:29
All I can say is it is a PERMUTATION problem and the

Any brave souls want to reason how to get this answers

Kudos [?]: 107 [0], given: 0

Director
Joined: 28 Oct 2003
Posts: 501

Kudos [?]: 36 [0], given: 0

Location: 55405

### Show Tags

09 Jan 2004, 13:05
243= 3^5

So the identity of of the voter matters!

Kudos [?]: 36 [0], given: 0

Director
Joined: 03 Jul 2003
Posts: 651

Kudos [?]: 107 [0], given: 0

### Show Tags

09 Jan 2004, 13:18
stoolfi wrote:
243= 3^5

So the identity of of the voter matters!

Stoolfi
You are a genius!
Could you explain the second question?
Whak kind of permutation is it?
One thing I could not understand is that how small samples
such as 3 and 5 can give 243 permutations!

Could any one suggest any material in the web or books
that specifically explains these kind of (2 or more dimentional)
permutation problems?

Kudos [?]: 107 [0], given: 0

Director
Joined: 28 Oct 2003
Posts: 501

Kudos [?]: 36 [0], given: 0

Location: 55405

### Show Tags

09 Jan 2004, 13:35
Quote:
Could you explain the second question?

Yep. Three voters each vote for themselves, so just forget about them, ad there can only be one outcome as far as they are concerned.

As for the others, two voters, three choices apiece-- 3^2.

Quote:
Whak kind of permutation is it?

I just do the problems. I do not name names, here.

One thing I could not understand is that how small samples
such as 3 and 5 can give 243 permutations!

that little carat (^) is one powerful thing!

Quote:
Could any one suggest any material in the web or books
that specifically explains these kind of (2 or more dimentional)
permutation problems?

AkamaiBrah, who is certainly a greater GMAT genius than I, recommends the Schaum guides.

http://www.amazon.com/exec/obidos/tg/de ... 9?v=glance

http://www.amazon.com/exec/obidos/tg/de ... ce&s=books

If you search used bookstores, I'm sure they can be had pretty cheaply.

Kudos [?]: 36 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

### Show Tags

10 Jan 2004, 09:43
I thought it should be 5^3

Kudos [?]: 114 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

### Show Tags

10 Jan 2004, 09:49
5^3 does not make sense. Three candidates are included in the voters. I read the q wrong.
I take it back

Kudos [?]: 114 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

### Show Tags

10 Jan 2004, 10:10

Let the candidates by C1,C2,C3 and voters be V1 and v2

C1 can get C1, C1V1, C1V2, C1V1V2 the same thing applies for each candidate.
I get 9 combinations = 3C2 + 3

Kudos [?]: 114 [0], given: 0

Director
Joined: 28 Oct 2003
Posts: 501

Kudos [?]: 36 [0], given: 0

Location: 55405

### Show Tags

10 Jan 2004, 10:32
anand,

your post is unclear to me, but I'll try again to explain.

In the first case,

There are 3 candidates and 5 voters. In how many ways can the votes be given?

we have five voters who can make three different choices

Voter one can pick A, B, or C.
Voter two can pick A, B, or C.
Voter three can pick A, B, or C.
Voter four can pick A, B, or C.
Voter five can pick A, B, or C.

Second question:

If 3 candidates are included in 5 voters and they vote for themselves only, then how many ways of giving votes are possible?

Voter 1 is candidate 1. He votes 1.
Voter 2 is candidate 2. He votes 2.
Voter 3 is candidate 3. He votes 3.

Voter 4 is not a candidate. He votes 1, 2, or 3.
Voter 5 is not a candidate. He votes 1, 2, or 3.

Three possible votes, 2 times--------- 3^2

To illustrate:

1 2 3 1 1
1 2 3 1 2
1 2 3 1 3
1 2 3 2 1
1 2 3 2 2
1 2 3 2 3
1 2 3 3 1
1 2 3 3 2
1 2 3 3 3

Make sense yet?

Kudos [?]: 36 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

### Show Tags

10 Jan 2004, 10:36
Man I completely screwedup. I did get 9 for the second question
For the first question I did a stupid thing.

This is what it is

I thought c1 will pick v1 to v5 so I got 5^3. How can a candidate pick voters? It actually otherway
v1 will pick either c1,c2,c3.
So the answer has to be 3^5 because each voter can pick any tree and there are 5 voters.

yesterdays beer is still working on me. I need to go and take a swim.

Kudos [?]: 114 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

### Show Tags

10 Jan 2004, 10:41
If another condition is added saying a voter cannot vote for two different candidates at the same time then 3^5 wont be the answer. I hope you will agree.

Kudos [?]: 114 [0], given: 0

10 Jan 2004, 10:41
Display posts from previous: Sort by

# There are 3 candidates and 5 voters. In how many ways can

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.