Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 08 Sep 2010
Posts: 223
Location: India
WE 1: 6 Year, Telecom(GSM)

If four dice are thrown simultaneously,what is the probability that [#permalink]
Show Tags
27 Oct 2010, 05:59
1
This post received KUDOS
7
This post was BOOKMARKED
Question Stats:
63% (02:22) correct 38% (02:13) wrong based on 96 sessions
HideShow timer Statistics
If four dice are thrown simultaneously,what is the probability that the sum of the number is exactly 20? A. 35/1296 B. 55/1296 C. 51/1322 D. 61/533 E. 41/1321
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by ankitranjan on 27 Oct 2010, 23:15, edited 1 time in total.



Retired Moderator
Joined: 02 Sep 2010
Posts: 792
Location: London

Re: If four dice are thrown simultaneously,what is the probability that [#permalink]
Show Tags
27 Oct 2010, 12:59
5
This post was BOOKMARKED
ankitranjan wrote: If four dice are thrown simultaneously,what is the probability that the sum of the number is exactly 20?
1. 35/1296 2. 55/1296 3. 51/1322 4. 61/533 5. 41/1321
Consider KUDOS if u find it as a good question. We need a sum of 20. This can be achieved in the following ways : {5,5,5,5} > 1 way {5,5,4,6} > 4!/(2!) ways = 12 {4,4,6,6} > 4!/(2!2!) ways = 6 ways {3,5,6,6} > 4!/2! ways = 12 ways {2,6,6,6} > 4!/3! ways = 4 ways Total ways = 6x6x6x6 So probability = 35/1296 ... Answer (a)
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 30 Sep 2010
Posts: 56

Re: If four dice are thrown simultaneously,what is the probability that [#permalink]
Show Tags
28 Oct 2010, 06:37
Ok guys. I Have developed a much much easier way to find the solution and I need many KUDOS for this if you like it:
Dice problem
A nice way to find the sum:
e.g 4 dices are thrown
then the outcome of the sums can be:
4,5,6,………………14……………..,22,23,24
Mid point is 14. The left side of the mid point is mirror image of the right part.
So lets say the probability of getting a 20 is same as the probability of getting a 8
In this case the number of ways to get the sums are:
4: C(3,0) = 1 (start 1 before the # of throws) 5: C(4,1) = 4 6: C(5,2) = 10 7: C(6,3) = 20 8: C(7,4) = 35
So probability of getting a 20 = probability of getting a 8 = 35/6^4 = 35/1296 Similarly for rolloing of 3 dices:
then the outcome of the sums can be: Mid point is 10.5. The left side of the mid point is mirror image of the right part.
3,4,5,6,………………10.5……………..,15.16.17.18
In this case the number of ways to get the sums are:
3: C(2,0) = 1 (start 1 before the # of throws) 4: C(3,1) = 3 5: C(4,2) = 6 6: C(5,3) = 10 7: C(6,4) = 15 8: C(7,5) = 21



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11015
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If four dice are thrown simultaneously,what is the probability that [#permalink]
Show Tags
03 May 2017, 11:55
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Hi All, This question doesn't require any complex math at all; it can be solved with some arithmetic, some 'brute force' and a bit of logic: To start, each of the 4 dice has 6 possible outcomes (1, 2, 3, 4, 5 and 6), so there are 6^4 = 36^2 = 1296 total outcomes. Thus, the correct answer is either a fraction out of 1296 or a fraction that has been reduced from 1296. This allows you to immediately eliminate answers C, D and E. From the two remaining answers, there are either 35 or 55 dice combinations that will total 20. Using a bit of 'brute force', we can name the groups: 6662 6653 6644 6554 5555 Each of these groups has a certain number of possible outcomes. For example, 5555 can only occur 1 time, while 6662 can occur 4 times (2666, 6266, 6626 and 6662). At this point, you should note that 2 of the 5 possibilities yield just 1+4 = 5 options, so it's highly likely that the total number of possibilities is relatively small (in this case, 35 and not 55). If you wanted to list out all of the possibilities, then you could (and there would be 35 of them). If you 'time' your work, you could probably complete this step in 12 minutes. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 16 Jan 2013
Posts: 101
Location: Bangladesh
GMAT 1: 490 Q41 V18 GMAT 2: 610 Q45 V28
GPA: 2.75

Re: If four dice are thrown simultaneously,what is the probability that [#permalink]
Show Tags
28 Oct 2017, 16:37
What is the best way to ensure that l've considered all the possible scenarios? This time l didn't realize {4,4,6,6} is one of the possibilities. T_T
_________________
Heading towards perfection>>




Re: If four dice are thrown simultaneously,what is the probability that
[#permalink]
28 Oct 2017, 16:37






