1. The problem statement, all variables and given/known data How many different six-digit numbers are there whose three digits are even and three digits are odd? 2. Relevant equations No equations are required.We only need the principles of counting. 3. The attempt at a solution I tried to split into 4 cases: case I:there is no zero in the six digit number.such numbers =125*64*20 case II:there is one zero in the number.such numbers =125*16*5*10 case III:there are two zeroes in the number.such numbers =125*4*10*4 case IV:there are three zeroes in the number.such numbers =125*10 So the final answer will be 281250. But the correct answer is 179550. Can anyone show me where I have over counted ?