Love those repeated digits

let the numbers be a,a,b,b,c,d there 10c4 ways to select the 4 numbers 4c2 ways to select the 2 to be repeated 6!/2!2! ways to arrange them gives 226,800

now, the other combination. let the numbers be a,a,a,b,c,d then, 10c4 * 4c1 * 6!/3! = 100,800

adding gives 327,600.

now, 10% of these start with 0 - a five digit number so 9/10 * 327600 = 294840

Python brute force guess and check:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

def distinct(x):
    found = set()
    for i in str(x):
        found.add(i)
    return len(found)
count = 0
i = 100000
while i < 1000000:
    if distinct(i) == 4:
        count += 1
    i += 1
print count