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# Jack rolls 5 fair six-sided dice

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Jack rolls 5 fair six-sided dice. What is the probability that at least three dice show the same number?

Nov 1, 2020

#2
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6^5 =7776 possible outcomes (order counts)

N,A and B represent different numbers that can be thrown

NNNNN       6 ways

NNNNA       6*5*5 =150ways

NNNAA       6*5*5C2=30*10 = 300 ways

NNNAB       6*5*4 *5C2= 120*10= 1200 ways

1200+300+150+6 = 1656  (order counts)

P(at least 3 the same) =   1656/7776 = 23/108

I do not guarantee my answers, especially not counting and probability answers.

This answer does seem higher than I would have expected.

Nov 1, 2020

#1
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(5 nCr 3 * 5^2) + (5 nCr 4 * 5^1) + (5 nCr 5 * 5^0) = 276 / 6^5 =23 /648

[Sorry Melody. Didn't know you were working on it]

Nov 1, 2020
#4
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You did not need to appologize :)

Melody  Nov 1, 2020
#5
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Sorry, you got it spot on. It is: 1656 / 7776 =23 / 108. I just verified it by a computer code. The first stupid answer I worked out was for "at least 3 specific numbers, such as 3 ones"

Guest Nov 1, 2020
#6
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Thanks What coding language did you use?

One of these days I will learn to code in some modern language.

Melody  Nov 1, 2020
#9
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Thank you.

That sounds like a commonly used one.

I think some people use Python.

I guess when I am ready to learn I will work out the best one for me.

Melody  Nov 2, 2020
#2
+1

6^5 =7776 possible outcomes (order counts)

N,A and B represent different numbers that can be thrown

NNNNN       6 ways

NNNNA       6*5*5 =150ways

NNNAA       6*5*5C2=30*10 = 300 ways

NNNAB       6*5*4 *5C2= 120*10= 1200 ways

1200+300+150+6 = 1656  (order counts)

P(at least 3 the same) =   1656/7776 = 23/108

I do not guarantee my answers, especially not counting and probability answers.

This answer does seem higher than I would have expected.

Melody Nov 1, 2020
#7
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xxxxxxxxxx

Nov 1, 2020
edited by Guest  Nov 1, 2020