Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 00:32

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Tom is arranging his marble collection in a collector's case. He has

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56300
Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 25 Dec 2017, 01:52
1
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

42% (03:14) correct 58% (03:00) wrong based on 33 sessions

HideShow timer Statistics


Tom is arranging his marble collection in a collector's case. He has five identical cat-eyes, five identical sulphides, and three identical agates. If he can fit exactly five marbles into the case and must at least have one of each type, how many different ways can he arrange the case?

A. 120
B. 150
C. 420
D. 1,260
E. 1,680

_________________
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 25 Dec 2017, 21:55
3
Bunuel wrote:
Tom is arranging his marble collection in a collector's case. He has five identical cat-eyes, five identical sulphides, and three identical agates. If he can fit exactly five marbles into the case and must at least have one of each type, how many different ways can he arrange the case?

A. 120
B. 150
C. 420
D. 1,260
E. 1,680



hi..

so 5Cs, 5Ss and 3As..
atleast one of each C,S and A means TWO cases
I.. 3 of one kind and one each of other two
\(\frac{5!}{3!}=20\)
any one of 3 can be three, so 20*3=60
II... 2 of two and one of third
\(\frac{5!}{2!2!}=30\)
any one of 3 can be one, so 30*3=90

total 60+90=150

B
_________________
Intern
Intern
avatar
B
Joined: 30 Jul 2017
Posts: 20
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 28 Dec 2017, 13:18
Could someone pls provide more comprehensive explanation?
Manager
Manager
User avatar
S
Joined: 20 Feb 2017
Posts: 88
Location: United States
CAT Tests
Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 28 Dec 2017, 15:04
3
1
krikre wrote:
Could someone pls provide more comprehensive explanation?


Though explanation provided by Chetan is good, I am adding more details to his solution.

Tom has 5 cat-eys (say C) , 5 sulphides (say S) and 3 agates (say A).
So Tom has 5C, 5S and 3A.

The case can fit 5 marbles and please note the question is asking for the arrangement so the order of marbles in Case is also important.
As per the question. We must have 1C, 1S and 1A.
so for remaining 2 spots -
We can Choose 2 of one kind or 1 of two kinds.

1. If we choose 2 of one kind -
We can choose 2 of one kind in 3 ways ( Either 2C or 2A or 2C)
So in total in case, we will have 3 of one kind and 2 other kinds of marble
There is a formula to solve these kinds of arrangement but in case somebody doesn't recall -
We can arrange the 1 kind in 5 ways and second kind by 4. We have 3 identical marble left and 3 spots to fill so the order is not important now.
So ways = 5X4 = 20
so total ways as we can select first 2 marble in 3 ways
= 5X4X3 = 60

2. If we choose 2 kinds of marble to fill 2 empty spaces -
Now we can choose marble in 3 ways ( 1A and 1C, 1A and 1S, 1S and 1C).
So in case, we will 2-2 marbles of 2 kinds and 1 marble of one kind.
Lets' assume we have 2A, 2S and 1C.
for 1C, we can select spots in 5 ways.
for 2As, we can select spots in 6 ways (Select 2 out of 4, order not important).
for remaining 2S, we are left with 2 spots only after fixing 1C and 2As, so only one way.
So ways = 6X5 = 30
so total ways as we can select first 2 marble in 3 ways
= 30X3 = 90.

Total ways = Case 1 + Case 2 = 60 + 90 = 150

Note - It may be easier to solve with the formulas if you are aware of them.
_________________
*****************************************************************
Kudos are always welcome.
Manager
Manager
User avatar
P
Joined: 13 Jun 2012
Posts: 205
Location: United States
WE: Supply Chain Management (Computer Hardware)
GMAT ToolKit User CAT Tests
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 28 Dec 2017, 16:55
2
krikre wrote:
Could someone pls provide more comprehensive explanation?



This has helped me a lot. Hopefully will help you.

https://www.youtube.com/watch?v=QCq6qRJCTj8
Intern
Intern
avatar
B
Joined: 30 Jul 2017
Posts: 20
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 30 Dec 2017, 15:57
Hello Lostin and Turkish, thank you for your responses.

Lostin could you kindly let me know what formulas you mean ?

Thank you.
Manager
Manager
User avatar
S
Joined: 20 Feb 2017
Posts: 88
Location: United States
CAT Tests
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 30 Dec 2017, 16:40
1
krikre wrote:
Hello Lostin and Turkish, thank you for your responses.

Lostin could you kindly let me know what formulas you mean ?

Thank you.


Chetan has used the same formulas for solutions, very handy and fast in case of big numbers.
Attachments

File comment: Arrangement/Selection having identical entities -
Identical_arrangements.JPG
Identical_arrangements.JPG [ 28.9 KiB | Viewed 804 times ]


_________________
*****************************************************************
Kudos are always welcome.
Intern
Intern
avatar
B
Joined: 30 Jul 2017
Posts: 20
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 30 Dec 2017, 17:03
Thank you very much for your time, very helpful!
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11713
Re: Tom is arranging his marble collection in a collector's case. He has  [#permalink]

Show Tags

New post 05 Jul 2019, 09:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Tom is arranging his marble collection in a collector's case. He has   [#permalink] 05 Jul 2019, 09:41
Display posts from previous: Sort by

Tom is arranging his marble collection in a collector's case. He has

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne