Q: Count the number of passwords with following constraints. Assuming digits = {0, 1, …..9},

Question

letters = {a, b, ….. y, z}
(a) 5 characters which are digits or letters.
(b) 4 characters which are digits or letters, with at least 1 digit.
(c) 4 characters which are digits. Adjacent characters are not the same.
(d) 6 characters which are letters. The first half must not equal to the last half.

Answer 1

(a) 36^5
(b) 10*36^4
(c) 10*9*9*9
(d) assuming you just mean that the exact sequence of 3 letters does not repeat, then 36P3 * (36P3 - 1)

extra credit: what if you mean that the first 3 letters do not all repeat in the 2nd half of the password?

Answer 2

36P3 * (36-1 * 35-1 * 34-1)
is it correct.