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

It is currently 16 Sep 2014, 01:35

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

Permutations???

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 15 Apr 2007
Posts: 38
Followers: 0

Kudos [?]: 10 [0], given: 0

Permutations??? [#permalink] New post 31 Aug 2008, 18:04
I am having problems with this question:

The US Senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed.

(a) How many different committees are possible?
(b) How many committees are possible if no state may have more than one senator on the committee?
(c) What’s the probability that no state will have both of its senators on a committee?

I think the first (a) should be: 100*99*98*97*96

But I'm not sure about (b) and (c). Help.
CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2501
Followers: 53

Kudos [?]: 505 [0], given: 19

GMAT Tests User
Re: Permutations??? [#permalink] New post 31 Aug 2008, 19:21
kamilaak wrote:
I am having problems with this question:

The US Senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed.

(a) How many different committees are possible?
(b) How many committees are possible if no state may have more than one senator on the committee?
(c) What’s the probability that no state will have both of its senators on a committee?

I think the first (a) should be: 100*99*98*97*96

But I'm not sure about (b) and (c). Help.

a. 100c5 = (100x99x98x97x96x95!)/(5x4x3x2x1x95!) = 5x33x49x97x96
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Current Student
User avatar
Joined: 11 May 2008
Posts: 559
Followers: 7

Kudos [?]: 22 [0], given: 0

GMAT Tests User
Re: Permutations??? [#permalink] New post 31 Aug 2008, 19:36
well, let me try my luck..



2)if no state may have more than one senator on the committee ---->

if only 50 senators are available to form commitee , then 50c3 = 50*49*48/3*2*1 = 19600.

3) What’s the probability that no state will have both of its senators on a committee?---->
5/100*4/98*3/96*2/94*1/92= something im not interested in..
is the method ok??
Intern
Intern
avatar
Joined: 15 Apr 2007
Posts: 38
Followers: 0

Kudos [?]: 10 [0], given: 0

Re: Permutations??? [#permalink] New post 31 Aug 2008, 19:58
why 50C3?

Should it be 50C5? Since we have 5 person committee?
SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1829
Location: New York
Followers: 26

Kudos [?]: 450 [0], given: 5

GMAT Tests User
Re: Permutations??? [#permalink] New post 31 Aug 2008, 21:14
kamilaak wrote:
I am having problems with this question:

The US Senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed.

(a) How many different committees are possible?
(b) How many committees are possible if no state may have more than one senator on the committee?
(c) What’s the probability that no state will have both of its senators on a committee?

I think the first (a) should be: 100*99*98*97*96

But I'm not sure about (b) and (c). Help.


a)
100C5
b)

= 100*98*96*94*92 /5!
(First we can chose any senator(100 ways)* (one senator already chosen and we can't chose another senator from the same state so 98 members left)*....)

c)

p = (100*98*96*94*92 /5! ) / 100C5

What is OA
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning


Last edited by x2suresh on 04 Sep 2008, 06:19, edited 1 time in total.
Current Student
User avatar
Joined: 11 May 2008
Posts: 559
Followers: 7

Kudos [?]: 22 [0], given: 0

GMAT Tests User
Re: Permutations??? [#permalink] New post 31 Aug 2008, 22:01
oh!!, yes i meant 50c5..
Manager
Manager
avatar
Joined: 22 Jul 2008
Posts: 154
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: Permutations??? [#permalink] New post 03 Sep 2008, 14:54
1) 100 C 5

2) 50 C 5 * (2 C 1)^5

3) 2)/1) i.e., 50 C 5 * (2 C 1)/100 C 5
Re: Permutations???   [#permalink] 03 Sep 2008, 14:54
    Similar topics Author Replies Last post
Similar
Topics:
1 permutations tarek99 2 23 Aug 2009, 00:51
Permutation jugolo1 2 25 Sep 2008, 13:03
Permutation pawan82 8 03 Jul 2007, 06:32
Permutations deowl 17 07 Jun 2006, 08:58
Permutation? john2005 5 29 Mar 2006, 19:46
Display posts from previous: Sort by

Permutations???

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.