Answer to Question #190529 in Discrete Mathematics for Good boy

Question

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.

Answer 1

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$=50\times 4\times 26\times 5263=7311600$