We want to make a 6 character password such that the password must start and end with a digit. Moreover, one digit must be even and other must be odd. There must be one capital letter. How many such password can we make? Note: Characters for password can be Capital letters, Small letters and Digits.

First and last place are digits.

one is even and other odd.

So first place can fill with 2,4,6,8,0 So 5 ways

Last place can fill with 1,3,5,7,9 So 5 ways

But the Places can permute that First pace can be filled with odd and last with even.

SO Overall ways to fill first and Last Place $= 5\times 5\times 2=50 ways$

The middle 4 places choose one place for capital letter and It has 26 option and remaining 3 places each has 52 options.(26 small + 26 capital)

Total Number of ways$=50\times 4\times 26\times 5263=7311600$