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If four dice are rolled, what is the probability that at least two of

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Noida
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If four dice are rolled, what is the probability that at least two of [#permalink] If four dice are rolled, what is the probability that at least two of   13 May 2024, 00:10
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48% (01:54) correct 52% (02:29) wrong based on 23 sessions
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If four dice are rolled, what is the probability that at least two of Them show the same face?

­A) 37/72
B) 11/36
C) 47/72
D) 25/36
E) 13/18
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Noida
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Re: If four dice are rolled, what is the probability that at least two of [#permalink] If four dice are rolled, what is the probability that at least two of   13 May 2024, 00:14
I tried solving the following way but didn’t get the correct answer:

1 - (None has the same face) = 1 - (ALL faces are different)
1 - (6C4)/(6^4) = 1 - (5/432)

Can anyone guide why this is wrong?

Also, why can’t we choose all the different faces as

6C1 * 5C1 * 4C1 * 3C1

But this is different from 6C4?
Do we need to arrange them as 4! 
Should it be 6C4 * 4!

Please guide on how to select four different faces?
And how to solve by this approach?­
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YB10
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Re: If four dice are rolled, what is the probability that at least two of [#permalink] If four dice are rolled, what is the probability that at least two of   13 May 2024, 00:47
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6P4 and not 6C4, as the order in which they come don’t matter
Noida wrote:
I tried solving the following way but didn’t get the correct answer:

1 - (None has the same face) = 1 - (ALL faces are different)
1 - (6C4)/(6^4) = 1 - (5/432)

Can anyone guide why this is wrong?

Also, why can’t we choose all the different faces as

6C1 * 5C1 * 4C1 * 3C1

But this is different from 6C4?
Do we need to arrange them as 4! 
Should it be 6C4 * 4!

Please guide on how to select four different faces?
And how to solve by this approach?­


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AleenBola
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Re: If four dice are rolled, what is the probability that at least two of [#permalink] If four dice are rolled, what is the probability that at least two of   01 Jun 2024, 00:01
Total possible outcomes when rolling four dice:
Each die has 6 faces, so there are:
6^4=1296, possible outcomes when rolling four dice.

Calculate the number of outcomes where all dice show different faces:
The first die can show any of the 6 faces.
The second die can show any of the remaining 5 faces (different from the first die).
The third die can show any of the remaining 4 faces (different from the first two dice).
The fourth die can show any of the remaining 3 faces (different from the first three dice).
Therefore, the number of ways in which all four dice show different faces is:
6×5×4×3=360

Calculate the probability that all dice show different faces:The probability 𝑃(all different) divided by the total number of outcomes:
𝑃(all different)=360/ 1296=5/18

Calculate the probability that at least two dice show the same face:
𝑃(at least two the same)=1−𝑃(all different)=1−5/18=13/18
gmatclubot
Re: If four dice are rolled, what is the probability that at least two of [#permalink]
01 Jun 2024, 00:01
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Bunuel
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