Question

A password or PIN consisting of a string of exactly five digits is randomly generated. How many such passwords have exactly one digit being repeated once ?

Answer 1

Solution.

There are Total digits = 10

We have to make a PIN Code of 5 digits, in which there are 4 different digits and 1 is repeated.

So, required number of passwords = 10C4 *10C1 * 5!/2!

                                                       

Answer 2

Number of passwords that have exactly one digit being repeated once:-

We can calculate this as shown:-

If all the digits were different then the no. Of ways should have been = 10 × 9 × 8 × 7 × 6

But as one digit should repeat so it will be = 10 × 10 × 9 × 8 × 7

= 50400 passwords