orbs in a sack

Expert replies

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Apr 24, 2010 12:45 am

Bernard has 3 green, 2 red, and 3 blue orbs in a sack. He aimlessly elects to choose 5 orbs out of the sack, without replacement. What is the probability that of the 5 drawn orbs, he has picked 1 red, 2 green, and 2 blue orbs?
(A) 3/280
(B) 9/280
(C) 3/28
(D) 9/28
(E) 27/28

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Like this post

Source: Beat The GMAT — Problem Solving | Sat Apr 24, 2010 12:45 am

pradeepkaushal9518: Legendary Member; Posts: 1309; Joined: Wed Mar 17, 2010 11:41 pmFollowed by: 5 members; Thanked: 33 times

by pradeepkaushal9518 » Sat Apr 24, 2010 1:21 am

what i understand

5 out of 8 is 8C5= 8*7*6

1 red out of 2 red = 2C1=2
2 green out of 3 = 3C2= 3
2 blue out of 3= 3C2=3
probability= possible outcomes/total outcomes

= 2*3*3/8*7*6
= 3/56

which i dont find in option or i am doing any mistake

Like this post

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Apr 24, 2010 1:53 am

pradeepkaushal9518 wrote:what i understand

5 out of 8 is 8C5= 8*7*6

1 red out of 2 red = 2C1=2
2 green out of 3 = 3C2= 3
2 blue out of 3= 3C2=3
probability= possible outcomes/total outcomes

= 2*3*3/8*7*6
= 3/56

which i dont find in option or i am doing any mistake

We can get 1 Red-2 Green-2 Blue in many different ways (as the order does not matter).

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Like this post

rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Sat Apr 24, 2010 2:32 am

We can select 5 orbs out of 8 in 8 C 5 ways = 8!/ (5!x2!) = 56 .

So Number of possible ways = 56 .

Now we can select a red orb in 2 ways as there are only 2 red orbs .

2 green in 3C2 ways = 3 ways .

2 blue in 3C2 ways = 3 ways .

Number of desired out come = 2 x 3 x 3 = 18 .

Number of possible out come = 56 .

Probability = Number of desired out come / Number of possible out come .

Probability= 18 / 56 [spoiler]= 9 / 28 that is D .[/spoiler]

"Know thyself" and "Nothing in excess"

Like this post

Fiver: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Sep 22, 2008 3:51 am; Thanked: 8 times; GMAT Score:680

by Fiver » Sat Apr 24, 2010 6:54 am

Agree with D.
Here's another approach.
Total no. of items is 8
P (1R, 2G & 2B) without replacement = 2/8 * 3/7 * 3/6 = 3/56
And since the order does not matter there are 3! possible orders.
Hence our answer is (3/56) * 6 = 9/28

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review