Question

Consider making a four-digit I.D. number using the digits 3,5,8, and 0
a. How many I.D. numbers can be formed using each digit once?
b. How many can be formed using each digit once and not using 0 first?
c. How many can be formed if repetition is allowed and any digit can be first?
d. How many can be formed if repetition is allowed but 0 is not used first?

Answer 1

a) so we can use the 0 at the front
number of ways = 4x3x2x1 = 24
b) can't have zero at front
number of ways = 3x3x2x1 = 18
c) repeats are allowed and zero can be at front
number of ways = 4x4x4x4= 256
d) repeats allowed but no zero at front
number of ways = 3x4x4x4 = 192