A four-character password to log onto a computer is drawn from the digits 0-9 and a subset of 23 letters of the alphabet (repetition is permitted). Determine the number of passwords possible if
a) the letters used are not case sensitive (that is, a lowercase letter is treated the same as an uppercase letter).
b) the letters used are case sensitive (that is, an uppercase letter is considered different than the same lowercase letter).

a) the answer is 33*33*33*33= 1185921

b) the answer is 56*56*56*56= 9834496

Step-by-step explanation:

a) since the letters used are not case sensitive and repetition is allowed we have 33 options.

The 0-9 digits are 10 digits in total and the 23 letters gives us= 23+10= 33 options

Getting a four character password with repetition gives us

33*33*33*33= 1185921

b) The letters used are case sensitive and repetition allowed we have 56 options

23+23+10= 56

Getting a four character password

56*56*56*56= 9834496

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.