A fair six-sided die is rolled 6 times. What is the probability of get

Question

A fair six-sided die is rolled 6 times. What is the probability of getting 1, 2, 3, 4, 5, and 6 in no particular order ?

A. 1/216
B. 5/216
C. 5/324
D. 1/7,776
E. 1/46,656

gmatophobia · Answer

The first roll can be any number.

The second can be any but the first so only has a 5/6 chance of success.

The third roll has only a 4/6 chance and so on until the 6th roll which has only a 1/6 chance.

So, the overall probability is 5/6* 4/6 *3/6 * 2/6*1/6 = 5 / 324

IMO - C

sydqur · Answer

C

1/1 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 5/324

BrushMyQuant · Answer

Given that A fair six-sided die is rolled 6 times, and we need to find What is the probability of getting 1, 2, 3, 4, 5, and 6 in no particular order ?

Now in each outcome we can get numbers from 1 to 6 => 6 possibilities

In the First Roll   we can get any number out of 1 to 6 in 1 way. (As some number will come for sure)

In the Second Roll   chances of getting any of the remaining numbers from (2, 3, 4, 5, 6) =  \frac{5}{6}  (As there are 5 choices out of 6 in which this can happen)

In the Third Roll   chances of getting any of the remaining numbers (apart from the ones we got in the previous rolls) =  \frac{4}{6}  (As there are 4 choices out of 6 in which this can happen)

In the Fourth Roll   chances of getting any of the remaining numbers (apart from the ones we got in the previous rolls) =  \frac{3}{6}  (As there are 3 choices out of 6 in which this can happen)

In the Fifth Roll   chances of getting any of the remaining numbers (apart from the ones we got in the previous rolls) =  \frac{2}{6}  (As there are 2 choices out of 6 in which this can happen)

In the Sixth Roll   chances of getting any of the remaining numbers (apart from the ones we got in the previous rolls) =  \frac{1}{6}  (As there are 1 choices out of 6 in which this can happen)

=>   Probability of getting 1, 2, 3, 4, 5, and 6 in no particular order   = Product of above six probabilities = 1 *  \frac{5}{6}  *  \frac{4}{6}  *  \frac{3}{6}  *  \frac{2}{6}  *  \frac{1}{6}  =  \frac{5}{324}

So,  Answer will be C 
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

Regor60 · Answer

There are 6^6 possible arrangements of outcomes.

1 through 6 can be arranged in

6! ways

Probability is therefore:

6!/6^6 = 5!/6^5 = 5*4/6^4 =

20/1296 = 10/648 = 5/324

Posted from my mobile device

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A fair six-sided die is rolled 6 times. What is the probability of get

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