Question

Suppose that a "code" consists of 5 digits, none of which is repeated. (A digit is one of the 10 numbers 0,1 2,3 4,5 6,7 8,9.)

How many codes are possible?

Answer 1

As repetition is not allowed, the number of codes here is computed as:

_ _ _ _ _

The number of ways to fill the first digit is 10 ways here as there are 10 digits possible here. As we have already filled the first digit, there would be 9 ways to fill the second digit. and so on..

Therefore the number of 5 digit codes here is computed as:
= 10*9*8*7*6

= 30240

Therefore there are 30240 codes possible here.