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# Counting books

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Intern
Joined: 03 May 2003
Posts: 28
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10 Aug 2003, 08:55
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can someone please explain the solution to this problem.

There are 10 books on a shelf. 4 of them have a soft cover and 6 of them have a hard cover. In how many ways can you remove 5 books from the shelf so as to have at least one soft covered book and at least one hard covered book.
SVP
Joined: 03 Feb 2003
Posts: 1604
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10 Aug 2003, 10:24
5(all)-5(soft)-5(hard)
10C5-0-6C5

Correct? After Akamaibrah crucified me on prime factorization, I start to doubt in any problem.
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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10 Aug 2003, 10:40
stolyar wrote:
5(all)-5(soft)-5(hard)
10C5-0-6C5

Correct? After Akamaibrah crucified me on prime factorization, I start to doubt in any problem.

Didn't mean to crush you on that problem. Just wanted to show your stubborn butt that giving someone a formula to get the answer is NOT the same as showing them how to solve the problem.

BTW, i got the same answer as you: 246. There is no reason to doubt when you have a rationale for coming up with your answer!
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

SVP
Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA
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21 Jan 2004, 19:45
S H
0 5 = 6C5 = 6
1 4 = 4C1 * 6C4 = 60
2 3 = 4C2 * 6C3 = 120
3 2 = 4C3 * 6C2 = 60

Total = 246
Director
Joined: 03 Jul 2003
Posts: 652
Followers: 3

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22 Jan 2004, 10:19
anandnk wrote:
S H
0 5 = 6C5 = 6
1 4 = 4C1 * 6C4 = 60
2 3 = 4C2 * 6C3 = 120
3 2 = 4C3 * 6C2 = 60

Total = 246

Anand the collection should have atleast one S and atleast one H.
SVP
Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA
Followers: 6

Kudos [?]: 101 [0], given: 0

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22 Jan 2004, 15:24

S H

1 4 = 4C1 * 6C4 = 60
2 3 = 4C2 * 6C3 = 120
3 2 = 4C3 * 6C2 = 60
4 1 = 4C4 * 6C1 = 6

Total = 246
22 Jan 2004, 15:24
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