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

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Bunuel
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A fair six-sided die is rolled 6 times. What is the probability of get [#permalink] New post   02 Jan 2022, 05:10
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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

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gmatophobia
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Re: A fair six-sided die is rolled 6 times. What is the probability of get [#permalink] New post   02 Jan 2022, 06:06
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

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Re: A fair six-sided die is rolled 6 times. What is the probability of get [#permalink] New post   02 Jan 2022, 06:16
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Total possible outcome is \(6^6\). (1st roll has 6 possibilities,2nd has 6 possibilities and so on.. for 6 rolls)

Number of times 1,2,3,4,5,6 can appear is 6! ( arranging the 6 different numbers is 6! )

So, probability will be 6!/\(6^6\) = 5/324
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Re: A fair six-sided die is rolled 6 times. What is the probability of get [#permalink] New post   02 Jan 2022, 06:21
The probability of getting any particular set of numbers in a particular order is the same, (1/6)^6.

Given that no particular order matters, any one of the permutations of the set satisfies the question

6!(1/6)^6 = 5!/6^5= 120/7776

= 5/324

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Re: A fair six-sided die is rolled 6 times. What is the probability of get [#permalink]
02 Jan 2022, 06:21
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