There are 12 books - A, B, C,......K, L in a shelf. In how many ways can 5 books be selected?
A) A and C cannot be selected together
B) If A is selected, then C must also be selected
Answers are A->912 , b->372
Permutaion and Combination- Books arrangemnt
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Sat Apr 19, 2014 5:24 am
- Quasar Chunawala
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Wed Apr 16, 2014 9:41 pm
- Thanked: 4 times
B. No. of ways to select 5 out of 12 books(such that if A is selected, C also must be selected)
(i) Suppose A is selected, then C is also selected.
C(10,3) ways
(ii) Suppose A is not selected, then C is also not selected.
C(10,5) ways
Total number of ways = C(10,3) + C(10,5) = 120 + 252 = 372
Not sure however, if my answer for (A) tallies, with what is mentioned.
(i) Suppose A is selected, then C is also selected.
C(10,3) ways
(ii) Suppose A is not selected, then C is also not selected.
C(10,5) ways
Total number of ways = C(10,3) + C(10,5) = 120 + 252 = 372
Not sure however, if my answer for (A) tallies, with what is mentioned.
-
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Sat Apr 19, 2014 5:24 am
Hi Quasar,
Thanks a lot for heads up
Case 1: With A selected there are 11c4 ways which is 330
Case 2: With C selected there are 11c4 ways which is 330
Case 3: With A and C not selected there are 12C5 ways which is 252
Hence [spoiler]Case1+Case2+Case3 = 912[/spoiler]
For B:
Case 1: With A and C must be selected there are 10c3 ways which is 120
Case 2: With A and C not selected there are 10c5 ways which is 252
Hence [spoiler]Case1+Case2 = 372[/spoiler]
Got the answer after trying the same questions 15 minutes later
Thanks a lot for heads up
For A:There are 12 books - A, B, C,......K, L in a shelf. In how many ways can 5 books be selected?
A) A and C cannot be selected together
B) If A is selected, then C must also be selected
Case 1: With A selected there are 11c4 ways which is 330
Case 2: With C selected there are 11c4 ways which is 330
Case 3: With A and C not selected there are 12C5 ways which is 252
Hence [spoiler]Case1+Case2+Case3 = 912[/spoiler]
For B:
Case 1: With A and C must be selected there are 10c3 ways which is 120
Case 2: With A and C not selected there are 10c5 ways which is 252
Hence [spoiler]Case1+Case2 = 372[/spoiler]
Got the answer after trying the same questions 15 minutes later
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
s91arvindh wrote:There are 12 books - A, B, C,......K, L in a shelf. In how many ways can 5 books be selected?
Q1: A and C cannot be selected together
Q2: If A is selected, then C must also be selected
Q1: A and C cannot both be selected
GOOD combinations = (ALL possible combinations - (BAD combinations with both A and C)
ALL:
Number of ways to choose 5 books from 12 options = 12C5 = (12*11*10*9*8)/(5*4*3*2*1) = 11*9*8 = 792.
BAD:
In a bad combination, 3 books are chosen to be combined with A and C.
From the 10 remaining books, the number of ways to choose 3 to be combined with A and C = 10C3 = (10*9*8)/(3*2*1) = 120.
GOOD:
792-120 = 672.
Q2: If A is selected, C is also selected
Case 1: A and C are both selected
As shown above, the number of ways to choose 3 books to be combined with A and C = 120.
Case 2: A is not selected
If A is not selected, it is still possible to select C.
From the 11 remaining books, the number of ways to choose 5 = (11*10*9*8*7)/(5*4*3*2*1) = 462.
Total ways = 120 + 462 = 582.
The OAs are incorrect.
What is the source of this problem?
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Please see my notes in red:
s91arvindh wrote:For A:There are 12 books - A, B, C,......K, L in a shelf. In how many ways can 5 books be selected?
A) A and C cannot be selected together
B) If A is selected, then C must also be selected
Case 1: With A selected there are 11c4 ways which is 330
Once A is chosen, we cannot choose C.
Thus, 10 books remain that could be combined with A.
From the 10 remaining books, the number of ways to choose 4 = 10C4 = 210.
Case 2: With C selected there are 11c4 ways which is 330
Once C is chosen, we cannot choose A.
Thus, 10 books remain that could be combined with C.
From the 10 remaining books, the number of ways to choose 4 = 10C4 = 210.
Case 3: With A and C not selected there are 10C5 ways which is 252
Hence Case1+Case2+Case3 = 210+210+252 = 672.
For B:
Case 1: With A and C must be selected there are 10c3 ways which is 120
Case 2: With A and C not selected there are 10c5 ways which is 252
As I noted in my solution above, if A is not selected, we may still select C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- Quasar Chunawala
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Wed Apr 16, 2014 9:41 pm
- Thanked: 4 times
GmatGuruNY,
For (A), in fact I deduced that
No. of ways of (not selecting A and C together) = Total - (no. of ways to have both A and C)
But, the answer caused doubt. You offered a very lucid explanation.
And that C may be selected, even if A isn't. Nice catch! I wish I'd have spotted that. Gee thanks!
I am a starter, I plan to take my GMAT soon. Look forward to a lot more fun...
For (A), in fact I deduced that
No. of ways of (not selecting A and C together) = Total - (no. of ways to have both A and C)
But, the answer caused doubt. You offered a very lucid explanation.
And that C may be selected, even if A isn't. Nice catch! I wish I'd have spotted that. Gee thanks!
I am a starter, I plan to take my GMAT soon. Look forward to a lot more fun...