Question

How many 4 digit pins have two  1's but you dont know where?

Answer 1

Since a pin is made of digits 0 to 9, A pin with two 1's but unknown locations can be made in 4C2*10*10=600 ways. The 2 locations where 1 will be placed is chosen in 4C2=6 ways,in the other 2 locations we have to take 1 choice from 10 choices of numbers (0-9) each , in 10*10=100 ways. Note, here my pin may start with 0 because ATM pins do start with 0 and also nowhere it is mentioned that 0 cannot be first digit. Hence a 4 digit Atm pin with two 1's can be chosen in 600 ways.