Say I have a random number generator that generates numbers between 0 and 9 inclusive (10 possibilities) and I run it 6 times. What I am trying to find is the probability that at least 5 of those 6 random numbers will be the same. I could think of 2 ways to find the answer, the first one: (10^6) is the total number of possible 6 digit numbers generated. The number of numbers that have the same 5 or 6 of the same digits will be 10*[ (6C5 + 6C6) ]. Where 6C5 is the number of choices for the locations of the 5 digits that are the same and 6C6 = 1 is for the possibility when all digits are the same). 10*[ (6C5 + 6C6) ] = 10*(6+1) = 70. The probability would then be 70/(10^6). The second way: This involves the number of combinations with repetition of picking out of 10 digits 6 times. The formula I found is (n+r-1)!/(r!(n-1)!) where in this case, n = 10 and r = 6. This gives me the total number of possible combinations after which I would divide 70 by that number to get the probability. However, in this case the number of possible combinations is 5005 instead of 10^6. I believe 5005 is wrong because the first way gives me an answer that I think is closer to the right answer. What exactly does the formula for combinations with repetition calculate? How can I use it in the above problem?