Jack rolls 5 fair six-sided dice. What is the probability that at least three dice show the same number?
+118608 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.
(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]
+118608 You did not need to appologize :)
Could you elaborate on your answer please.
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"
+118608 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.
