Question

How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.)
(a) do not contain the same digit twice?
(b) begin and end with a 1?

Answer 1

(a) Do not contain the same digit twice means all digits are different, so the first digit can be one of 10, the second of nine (we already used one), then 8, then 7, so multiplying rule says that we have 10*9*8*7=5040 combinations. Answer: 5040.

(b) If the number starts and ends with 1 then only 2 middle digits can be different and since both middle digits can be one of 10, we 10*10=100 combinations. Answer: 100.