If 6 digits ranging 0 to 9 are randomly generated, what are the odds that at least 4 of the digits are the same.

Question

Can someone at least give me a few tips on how to work this out? I don't even know if i should treat this like a combination or permutation.

Answer 1

The total number of possible ordered outcomes is 10^6. Let k be one of the digits. The probability that k occurs four or more times is the sum P_4 + P_5 +P_6 where each P_i is the probability that k occurs exactly i times. P_ i  = (6 choose i)*9^(6-i)/ 10^6 (since you just have to choose the i spaces where k will occur and then choose from among the 9 remaining digits for the remaining 6-i spaces). You can compute P_4 + P_5 +P_6 = 1270/10^6.  There are ten choices for k, and no two k can occur 4 or more times simultaneously, so we multiply this probability by 10 to get 12700/10^6 = .0127