I have the exact same question, but I have to do it for all 6 values of k. I understand why there are ways to pick 2 digits, but why are there ways to order them? I've been trying to work the problem out this way:
For each value of k, treat the number of possible numbers as a 6-digit base-k number, subtract the numbers that don't have k distinct digits, and finally multiply it by the number of possible values for each distinct digit. So, for example, if k=4, I'd work it out as:
The number of numbers in a base 4, 6-digit number, minus all the numbers with only 3 distinct digits, 2 distinct digits, and 1 distinct digit, and multiply it by the number of ways to choose those 4 digits.
I know my reasoning is wrong, because when I try the same idea for k=5, I get a value over 1 million, which is obviously impossible.
So how do you calculate the number of ways to order the digits? I get that 6! is because it's a 6-digit number, but what the denominator?