BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Combinatorics #4

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

Combinatorics #4

by papgust » Sun Oct 18, 2009 5:15 am
There are 5 blue socks, 4 red socks and 3 green socks in Debu's wardrobe. He has to select 4 socks from this set. In how many ways can he do so?

A. 245
B. 120
C. 495
D. 60

Solution and explanation pls?
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 124
Joined: Thu Jun 18, 2009 5:33 am
Thanked: 35 times

by NikolayZ » Sun Oct 18, 2009 8:37 am
Hey again !
We have 12 total socks.
The guy must choose 4 whatever-color socks. (I'm curious why 4?!! =) )
it is combinatorics problem, since order does not matter.

So, the formula for this problem is C=(Total!)/(n!(total-n)!), where n is the number of socks Debu must select.

12!/4!*8!=495.
I hope i didn't mix smth up.
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sun Oct 18, 2009 10:58 pm
Thanks NikolayZ,

OA is 495. Thanks for the explanation
Top
User avatar
2009 Beat The GMAT Scholarship Winner
Posts: 182
Joined: Sat Mar 22, 2008 7:35 pm
Thanked: 3 times
Followed by:2 members
GMAT Score:700+

by gkumar » Mon Oct 19, 2009 2:40 am
If the socks of same color are considered different, then we can arrange in C(12,4) which comes out to be (C) 495 as said above.

But if the socks of the same color are equivalent and hence we can not tell one color sock from another sock of the same color, then the total number of ways is much less. I am not sure how to do this part, but another blog said 14 without explanation.
Top
Master | Next Rank: 500 Posts
Posts: 153
Joined: Tue Jun 02, 2009 2:48 pm
Location: Ohio
Thanked: 16 times

by JeffB » Mon Oct 19, 2009 8:23 am
BTG Scholarship winner....Congratz.
Top
User avatar
2009 Beat The GMAT Scholarship Winner
Posts: 182
Joined: Sat Mar 22, 2008 7:35 pm
Thanked: 3 times
Followed by:2 members
GMAT Score:700+

by gkumar » Mon Oct 19, 2009 8:38 am
Regarding the number of DIFFERENT ways to get socks (e.g., one green sock is equivalent to another green sock), which is 14:
The number of ways three naturals number add up to 4 are: 4+0+0, 3+1+0, 2+2+0, 2+1+1. Since now order matters, we have to count how many different ways three number add up to 4 including order: 4+0+0, three ways; 3+1+0, six ways; 2+2+0, three ways; 2+1+1, three ways. So, in total, it would be 15; but we have counted even the GGGG configurations, which is not possible. so the answer is 14

(Thanks JeffB!)
Top
Post new topic Post Reply
• Page 1 of 1