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

 It is currently 22 May 2015, 20:17

### 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

# A book publisher received 4 horror stories, 5 romantic

Author Message
TAGS:
Director
Joined: 03 Jul 2003
Posts: 655
Followers: 2

Kudos [?]: 26 [0], given: 0

A book publisher received 4 horror stories, 5 romantic [#permalink]  05 Feb 2004, 08:53
A book publisher received 4 horror stories, 5 romantic stories and 3 comedy stories. He wants to put together a book, contemporary stories, that should have at least one romantic story and one comedy story. How many different combinations are possible?
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

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

A book publisher received 4 horror stories, 5 romantic stories and 3 comedy stories. He wants to put together a book, contemporary stories, that should have at least one romantic story and one comedy story.

So, the book must come with a romantic story and a comedy story-- we can add up to:
4 horror stories-- 1 way to choose zero, 4 ways to choose one, 6 ways to choose two, 4 ways to choose three, 1 way to choose four. 16 configurations
4 romantic stories-- 1 way to choose zero, 4 ways to choose one, 6 ways to choose two, 4 ways to choose three, 1 way to choose four. 16 configurations
3 comedy stories-- 1 way to choose zero, 3 ways to choose one, 3 ways to choose two, 1 way to choose three. 8 configurations.

16*16*8

2048.

I know there's a substantially easier way to solve this, but it escapes me right now.
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
Followers: 1

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

(2^5 - 1) * (2^3 - 1) * (2^4) = 3472
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

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

gmatblast- you are right. I see my mistake.
Manager
Joined: 16 Jan 2004
Posts: 65
Location: NJ
Followers: 1

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

gmatblast

how did you come up with this formula. can you please exaplain in more details.

My line of thinking was

At lease one romantic and one comedy can be arrenged in 5*3 = 15
and then the 4 horror could be 15*5 ways or books
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
Followers: 1

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

pakoo wrote:
gmatblast

how did you come up with this formula. can you please exaplain in more details.

My line of thinking was

At lease one romantic and one comedy can be arrenged in 5*3 = 15
and then the 4 horror could be 15*5 ways or books

Pakoo,

What you have done is I guess, number of combinations IF ALL THE STORIES ARE TO BE USED. And it does not reflect the given retstriction properly.

We do not need to use all the stories. The only constraint that is applicable here is we must have 1R + 1C in whatever combination we choose.

That being said,

The reasoning I applied is that if there are n objects, and if there is no restriction on the number of objects to be selected, we can choose the objects in 2^n ways. This includes 1 way of selecting 0 object. For exampl if you have 3 objects a, b, c, how many ways you can make the selection?:

No of ways to select 0 object - 1
Number of ways to select 1 object - 3 (a, b, c)
Number of ways to select 2 objects - 3 (ab, bc, ac)
Number of ways to select 3 objects -1 (abc)

Total = 8 = 2^3

In our example, we have H - 4, R - 5, AND C-3

Number of ways to select H = 2^4
Number of ways to select R = 2^5
Number of ways to select C = 2^3

But, we must select 1R and 1C, So we have to ignore 1 way of selecting 0 H and 1 way of selecting 0 C

So required number = (2^5 - 1) * (2^3 - 1) * (2^4) = 3472

Last edited by gmatblast on 05 Feb 2004, 12:15, edited 1 time in total.
Manager
Joined: 16 Jan 2004
Posts: 65
Location: NJ
Followers: 1

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

gmatblast:

Lucid Explanation. Thanks

I know nPr and nCr for selecting r objects out of n objects. But here how did you decide of applying 2^n formula for the selection of the objectds.

Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
Followers: 1

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

pakoo wrote:
gmatblast:

Lucid Explanation. Thanks

I know nPr and nCr for selecting r objects out of n objects. But here how did you decide of applying 2^n formula for the selection of the objectds.

I think I explained this by way of an example. Please refer the bold text part in my posting. The bold text is just the explanantion of how 2^n is used. It has nothing to do with this problem. The solution of this problem starts only after the bold portion.
Manager
Joined: 28 Jan 2004
Posts: 203
Location: India
Followers: 2

Kudos [?]: 14 [0], given: 4

Hey Gmatblast....ur expalanation of the topic is toooo cool man......
hey any reference for studying Probability and Permuations (Combinations). I am very week in these 2 areas.
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
Followers: 1

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

mdfrahim wrote:
Hey Gmatblast....ur expalanation of the topic is toooo cool man......
hey any reference for studying Probability and Permuations (Combinations). I am very week in these 2 areas.

http://www.gmatclub.com/members/courses ... lity.shtml

For more study material, I would suggest that you pick up high school math book that covers probability.
Senior Manager
Joined: 23 Aug 2003
Posts: 462
Location: In the middle of nowhere
Followers: 1

Kudos [?]: 12 [0], given: 0

Hey gmat_blast...that was awesome.... for the explanation.

Vivek.
_________________

"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

Similar topics Replies Last post
Similar
Topics:
2 GMAT First Attempt - A Horror Story 2 02 Jan 2014, 09:37
Letter of Recommendation Horror Stories 17 07 Dec 2009, 13:05
2 GMAT Horror Story!!! 12 12 Jun 2008, 00:17
Alinder's story, pre and post 1st take + Horror Story 19 04 May 2008, 21:32
GMAT - Horror Story - Unreportable Scores.... 13 21 Apr 2008, 11:24
Display posts from previous: Sort by