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

 It is currently 08 Mar 2014, 12:56

### 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 bakery currently has 5 pies and 6 cakes in its inventory

Author Message
TAGS:
Manager
Joined: 23 Oct 2011
Posts: 54
Location: Ukraine
Schools: LBS '14 (M)
GMAT 1: 650 Q44 V35
WE: Corporate Finance (Mutual Funds and Brokerage)
Followers: 2

Kudos [?]: 16 [0], given: 7

A bakery currently has 5 pies and 6 cakes in its inventory [#permalink]  01 May 2012, 12:34
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:45) correct 18% (00:01) wrong based on 11 sessions
A bakery currently has 5 pies and 6 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?

A 3/11
B. 25/77
C. 5/11
D. 7/11
E. 50/77
[Reveal] Spoiler: OA
Manager
Joined: 23 Oct 2011
Posts: 54
Location: Ukraine
Schools: LBS '14 (M)
GMAT 1: 650 Q44 V35
WE: Corporate Finance (Mutual Funds and Brokerage)
Followers: 2

Kudos [?]: 16 [0], given: 7

Re: A bakery currently has 5 pies and 6 cakes in its inventory [#permalink]  01 May 2012, 12:36
My calculation is the following:
5/11 * 4/10 * 3/9 * 6/8 * 5/7 = 5/77
but there is no such solution.
could you please explain why is this method incorrect?
Math Expert
Joined: 02 Sep 2009
Posts: 16813
Followers: 2770

Kudos [?]: 17572 [0], given: 2222

Re: A bakery currently has 5 pies and 6 cakes in its inventory [#permalink]  01 May 2012, 12:58
Expert's post
JubtaGubar wrote:
A bakery currently has 5 pies and 6 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?

A 3/11
B. 25/77
C. 5/11
D. 7/11
E. 50/77

Combination approach:

\frac{C^3_5*C^2_6}{C^5_{11}}=\frac{25}{77}, where:
C^3_5 is # of ways to chose 3 pies out of 5;
C^2_5 is # of ways to chose 2 cakes out of 6;
C^5_{11} is # of ways to chose 5 items out of total 5+6=11.

Probability approach:

We need the probability that the owner will select PPPCC: \frac{5!}{3!*2!}*(\frac{5}{11}*\frac{4}{10}*\frac{3}{9})*(\frac{6}{8}*\frac{5}{7})=\frac{25}{77}, we are multiplying by \frac{5!}{3!*2!} since PPPCC scenario can occur in number of ways: PPPCC, PPCPC, PCPPC, CPPPC, ... Notice that the number of occurrences of PPPCC basically is the number of arrangements of 5 letters PPPCC out of which 3 P's and 2 C's are identical, so it's \frac{5!}{3!*2!} .

Hope it's clear.
_________________
Current Student
Joined: 05 Jul 2011
Posts: 314
Location: United States (CA)
Concentration: Marketing, Entrepreneurship
GMAT 1: 620 Q39 V35
GMAT 2: 620 Q43 V33
GMAT 3: 730 Q50 V40
Followers: 8

Kudos [?]: 61 [0], given: 3

Re: A bakery currently has 5 pies and 6 cakes in its inventory [#permalink]  01 May 2012, 13:58
Thanks Bunuel for the concise explanation!
_________________

My GMAT Debrief : http://gmatclub.com/forum/third-time-s-a-charm-142800.html#p1145912
Quant Concept Videos : http://gmatlife.blogspot.com/2012/07/gm ... ideos.html
My GMAT Blog : http://gmatlife.blogspot.com/

Re: A bakery currently has 5 pies and 6 cakes in its inventory   [#permalink] 01 May 2012, 13:58
Similar topics Replies Last post
Similar
Topics:
A bakery estimates its predicted yearly expenditures on 12 27 Oct 2010, 17:25
1 A bakery in neighbohood X sells cakes that are very 1 01 Sep 2011, 20:22
A certain bakery sells six different-sized wedding cakes 2 04 Mar 2012, 14:12
10 A dog breeder currently has 9 breeding dogs. 6 of the dogs 16 05 May 2012, 18:55
1 A certain bakery has 6 employees. It pays annual salaries of 8 05 Mar 2013, 03:31
Display posts from previous: Sort by