An intuitive way of calculating the permutations w/o the multinomial co-efficient: For a 3 digit passcode, there must be 1 pair of repeated digits somewhere in

An intuitive way of calculating the permutations w/o the multinomial co-efficient: For a 3 digit passcode, there must be 1 pair of repeated digits somewhere in the 4 number sequence e.g. 1_1_, 11__, _11_ etc.. so 2 x 3 = 6 different pairs. This pair of repeated digits is any one of the 3 unique numbers e.g. 11__ or 22__ or 33__. For any pair of repeated digits, there are just 2 options left for how the other 2 digits must be arranged in the sequence of 4 e.g. xx12 or xx21. So 6 x 3 x 2 = 36. For a 2 digit passcode, there are 2^4 = 16 permutations, except since there must be at least 1 of each digit present, you have to subtract the 2 permutations with 4 repeated digits e.g. 0000 or 1111. So 16 - 2 = 14.