Each character in a password is either a digit [0-9] or lowercase letter [a-z]. how many valid passwords are there with the given restriction(s)?

length is 19. no character repeats. must contain: z, 1, 0, and 9.

ex: p(11, 4) * p(4, 3)

write permutations as: p(n, k)

C(32,15) * P(19,19)

Step-by-step explanation:

digits given =0,1,2,3,4,5,6,7,8,9

letters from a to z =a,b,c...x,y,z

Total of both digits and letters 10+26 = 38

In the question, it's stated that  

Length is 19. No character repeats. Must contain: z, 1, 0, and 9.

Therefore, since all password must include z, 1, 0, and 9. (let's denote the four of them as Ф) ,these four notations must be included and the remaining 15 (i.e (19-Ф)) is selected from the whole 32 characters as C(32,15)

Also, 15 and Ф can be arranged as =19! ways.

As such, the total permutations are;

C(32,15) * P(19,19)

b

step-by-step explanation:

b