In a certain digital control system the control command is r

In a certain digital control system, the control command is represented by a set of four hexadecimal characters. What is the total number of control commands that are possible? If each control command must have a unique prefix, i.e., starting from left to right no hex character must be repeated, how many control commands are possible?

Solution

a) Answer : 65536

Reason: total number of characters is 4. Hex range is 16.

It means each character can have 16 possible values

So maximum number of combinations is 16×16×16×16 = 65536

b) Answer :43680

Reason: If no character is to be repeated then maximum occurrences of the next character will be decremented. So the same logic used for the previous question becomes 16×15×14×13 = 43680.