Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 27 May 2017, 11:38

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Futuristic's gambling laboratory has decided that 6-sided

Author Message
Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

Futuristic's gambling laboratory has decided that 6-sided [#permalink]

### Show Tags

09 Sep 2006, 16:44
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Futuristic's gambling laboratory has decided that 6-sided dice are out of fashion, and creates dice that are 10 sided, with numbers from 1 to 10 on the faces.

How many different combinations of numbers can be found by throwing 3 of these dice together? Assume all dice are undistinguishable.

E.g.

1,9,8 (is the same as 9,8,1)
1,9,9
Manager
Joined: 11 Jan 2006
Posts: 230
Location: Arkansas, US
WE 1: 2.5 yrs in manufacturing
Followers: 1

Kudos [?]: 17 [0], given: 18

### Show Tags

09 Sep 2006, 17:10
It's 720

the first dice can face any fo the 10 digits.
The second dice can face 9 digits, leaving the 1 digit occurred in dice 1
The third dice can face 8 digits, leaving the 2 digits occurred in dice 1 and 2

SO v have a a totoal number of 10*9*8 number of digits that V can have = 720
Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

09 Sep 2006, 17:30
nope...the question does not say that they are all different values
Senior Manager
Joined: 14 Jul 2005
Posts: 402
Followers: 1

Kudos [?]: 28 [0], given: 0

### Show Tags

09 Sep 2006, 17:36
I think 120

1,9,8 is the same as 1,8,9 and 9,8,1

Hence answer = 10C3 = 10*9*8/3*2*1 = 120
Manager
Joined: 25 May 2006
Posts: 227
Followers: 1

Kudos [?]: 65 [0], given: 0

### Show Tags

09 Sep 2006, 18:03
Mmmm, thinking again Iâ€™m now gettin 340

10^3-(10P3)/2-300=340
_________________

Who is John Galt?

Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

09 Sep 2006, 19:15
gmatornot wrote:
I think 120

1,9,8 is the same as 1,8,9 and 9,8,1

Hence answer = 10C3 = 10*9*8/3*2*1 = 120

This is correct only if we assume all dice have different values. What if they all have same values....or 2 of 3 have the same values?

hint hint....
Manager
Joined: 25 May 2006
Posts: 227
Followers: 1

Kudos [?]: 65 [0], given: 0

### Show Tags

09 Sep 2006, 20:10
Ok, plz omit my previous posts.

If in the following e.g

1,9,3 and 1,3,9 and 3,1,9 and 3,9,1 and 9,1,3 and 9,3,1 --> counts as 1
9,9,1 and 1,9,9 and 9,1,9 --> counts as 1
9,9,9 --> counts as 1

Then itÂ´s
10C3 + (10*10) + 10 = 230
_________________

Who is John Galt?

Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

09 Sep 2006, 20:38
you're getting closer.....

of the cases in (10x10), are there any also falling into 3rd part (10)....
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1263
Followers: 29

Kudos [?]: 307 [0], given: 0

### Show Tags

11 Sep 2006, 02:49
There are three cases:

(1) All three show the same number - 10 cases
(2) Two dice are the same, one is different 10*9
(3) All three are different 10C3=10*9*8/(3*2)=10*12

Total 10*(1+9+12)=220

Last edited by kevincan on 11 Sep 2006, 13:45, edited 1 time in total.
Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

11 Sep 2006, 11:35
kevincan wrote:
There are three cases:

(1) All three show the same number - 10 cases
(2) Two dice are the same, one is different 10*9
(3) All three are different 10*9*8

Total 10*(1+9+72)=820

(3) All three are different 10*9*8

In the above calculation, why are you finding the number of permutations? The dice are identical.
Manager
Joined: 28 Aug 2006
Posts: 160
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

11 Sep 2006, 13:35
It would be 3^10. Using the following logic.

For 2 dice with 6 sides it is 2^6. So for 3 dice with 6 faces it is 3^6.Hence for 3 dice with 10 faces it is 3^10.
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1263
Followers: 29

Kudos [?]: 307 [0], given: 0

### Show Tags

11 Sep 2006, 13:46
Futuristic wrote:
kevincan wrote:
There are three cases:

(1) All three show the same number - 10 cases
(2) Two dice are the same, one is different 10*9
(3) All three are different 10*9*8

Total 10*(1+9+72)=820

(3) All three are different 10*9*8

In the above calculation, why are you finding the number of permutations? The dice are identical.

You're right- I've corrected my answer! My holiday was too long
Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

11 Sep 2006, 13:48
Again, kevin shows us the light. The OA is 220.
VP
Joined: 02 Jun 2006
Posts: 1261
Followers: 2

Kudos [?]: 87 [0], given: 0

### Show Tags

11 Sep 2006, 14:04
Why is this not

10x10x10/3!

What are we overcounting in this case?

Thanks/
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1263
Followers: 29

Kudos [?]: 307 [0], given: 0

### Show Tags

11 Sep 2006, 14:19
Futuristic wrote:
Again, kevin shows us the light. The OA is 220.

Sorry about my mistake! Nice question- where did you get it-did you make it up?
Director
Joined: 28 Dec 2005
Posts: 752
Followers: 2

Kudos [?]: 16 [0], given: 0

### Show Tags

11 Sep 2006, 14:47
yes kev, i made it up. i found another question similar to this with 3 regular dice....and just adapted it a little to make it more interesting.

for those that are interested, with 3 regular dice there are 56 possibilities in all....
11 Sep 2006, 14:47
Display posts from previous: Sort by