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1) One has three fair dice and rolls them together. What is [#permalink]

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17 Aug 2003, 01:38

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(1) One has three fair dice and rolls them together. What is the probability of having two same numbers and one different? (for example, 2-2-6, 1-3-3, 6-5-6, and so on)

(2) One has four fair dice and rolls them together. What is the probability of having all the numbers different? (for example, 1-2-3-4, 6-5-4-1, and so on)

(3) One has six fair dice and rolls them together. What is the probability of having all the numbers different?

mmmmm, lets see...
1. total number of possibilities=6*6*6/3!
number satisfying 2 equal numbers=6*1*5/3!
answer: 5/36
2. total number of possibilities=6^4/4!
number satisfying 0 equal numbers=6*5*4*3/4!
answer: 10/36
3. total number of possibilities=6^6/6!
there is only one way of having different numbers, dont need to calculate that
answer: 1/(6^6/6!)

I would like to have the explanation for the 1st one.

I tried the following:-
1) Total no. of possibilities = 6*6*6 = 216
No. of events where all the three are equal = 6
No. of events when none are eqaul = 6*5*4 = 120
Therefore the no. of events when two are equal and third different
= 216-6-120 = 90

Therefore Probability that 2 are equal and third is different = 90 / 216
= 5/12

The remaining two I got the answers same as 5/18 and 5/324 respectively.

I would like to have the explanation for the 1st one.

I tried the following:- 1) Total no. of possibilities = 6*6*6 = 216 No. of events where all the three are equal = 6 No. of events when none are eqaul = 6*5*4 = 120 Therefore the no. of events when two are equal and third different = 216-6-120 = 90

Therefore Probability that 2 are equal and third is different = 90 / 216 = 5/12

The remaining two I got the answers same as 5/18 and 5/324 respectively.

I agree with indiatimes on this one. My method was the same:

All three numbers the same we have 6/216.
All three different we have 120/216.
So the remainder is 90/216, reducing to 5/12.

first dice can be any number. Second dice must be the same (order does not matter) 1/6. Third dice must be any number but not the same as in 1 and 2, so 5/6

first dice can be any number. Second dice must be the same (order does not matter) 1/6. Third dice must be any number but not the same as in 1 and 2, so 5/6