Question

1. How many different five-digit codes can be created if no digit can repeat? How many if the digits can repeat?

Answer 1

Solution:

Consider no digit can repeat in five-digit codes, then

First digit can be filled by 10 ways.

Second digit can be filled by 9 ways.

Third digit can be filled by 8 ways.

Fourth digit can be filled by 7 ways.

Fifth digit can be filled by 6 ways.

So, required number of ways = 10*9*8*7*6 = 30240

Required number of ways = 30240

If digit can repeat, then each code can be filled by 10 ways.

So, required number of ways = 10*10*10*10*10 = 100000

Required number of ways =100000