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

Guest Nov 1, 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

#1**+1 **

(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]

Guest Nov 1, 2020

#5**0 **

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

#2**+1 **

Best Answer

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