You are asked to create a fourcharacter password for an acco

You are asked to create a four-character password for an account. How many passwords are possible if:

A. If the four characters can only be numbers (digits)?

B. If the four characters can only be letters (not case sensitive)?

C. If the four letters cannot be repeated?

D. If the password can consist of any sequence of letters and/or numbers?

E. If there must be at least one number, and one letter?

Solution

A.

There are total 10 digits(0-9). Also there are 4 places to fill each of which can have 10 alternatives. Thus the total number of passwords = 10*10*10*10 = 10,000.

B.

There are total 26 digits(A-Z). Also there are 4 places to fill each of which can have 26 alternatives. Thus the total number of passwords = 26*26*26*26 = 456,976.

C.

If the four letters cannot be repeated then instead of all 4 places having 26 alternatives.Thus the total number of alternatives are 26*25*24*23 = 358,800.

D.

In this case for each place there are 36 alternatives(0-9 and A-Z). So total number of alternatives are 36*36*36*36 = 1,679,616.

E.

This Case consists of number of alternatives containing both numbers and letters together minus each of them seperately.Thus the number of alternatives = 1,679,616 - ( 456,976 + 10,000 ) = 1,212,640