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

Question

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 .

Bunuel · Accepted Answer

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.

D3N0 · Answer

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

AmoyV · Answer

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

Answer: D

Zhenek · Answer

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

tarunk31 · Answer

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.

Vaibhav21 · Answer

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

BrushMyQuant · Answer

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

As we are rolling three six-sided dice => Number of cases =  6^3  = 216

We need to get different number on each die
=> First dice can get any of the 6 numbers
=> Second dice can get any of the 5 numbers (Except the one which first dice got)
=> Third dice can get any of the 4 numbers ((Except the two numbers which the first and the second dice got)

=> Total number of ways = 6 * 5 * 4

=>  Probability of getting a different number on each die  =  \frac{6 * 5 * 4}{6^3}  =  \frac{5}{9}

So,  Answer will be D 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

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