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What is the probability of rolling three six-sided dice, and getting a

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What is the probability of rolling three six-sided dice, and getting a [#permalink]

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What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

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[Reveal] Spoiler: OA

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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

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New post 14 Apr 2015, 05:29
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three dices were rolled
total outcome 6x6x6
different number should appear on each
favorable outcome= 6c1*5c1*4c1

probability= favorable/total

ans=(6*5*4)/(6*6*6)= 5/9


ans= D
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

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New post 14 Apr 2015, 05:50
Bunuel wrote:
What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

Kudos for a correct solution.


6/6 * 5/6 * 4/6
=5/9

Answer: D

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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

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New post 14 Apr 2015, 09:26
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odds of rolling number on 1 dice is 1/6
odds of rolling another number on 2nd dice is 5/6
odds of rolling a number different from dice 1 and dice 2 on 3rd dice is 2/3
there are 6 total numbers so the resulting probability is
6*1/6*5/6*2/3 =10/18 = 5/9
D

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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

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New post 14 Apr 2015, 10:04
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1 Possible combinations with three different numbers on each die when three dies are rolled = 6*5*4
2 Total no. of combinations of numbers with three dies = 6*6*6

Divide 1 by 2 and we will get the probability = 6*5*4/6*6*6 = 5/9.

Therefore ans is D.
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

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New post 14 Apr 2015, 10:21
Prob of rolling 1st die and getting any number(Lets say x) = 6/6 = 1
Prob of rolling 2nd die and getting any number(Lets say y) but x = 5/6
Prob of rolling 2nd die and getting any number(Lets say z) but x and y = 4/6
Total prob = 1 x 5/6 x 4/6 = 5/9
Ans D

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What is the probability of rolling three six-sided dice, and getting a [#permalink]

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New post 20 Apr 2015, 06:26
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Bunuel wrote:
What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION

For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.

6 x 5 x 4 = 120 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6 = 216).

120/216 = 5/9

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

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Re: What is the probability of rolling three six-sided dice, and getting a   [#permalink] 25 Oct 2017, 07:01
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