An automated teller machine ATM requires a four digit person

An automated teller machine (ATM) requires a four digit personal identification number (PIN), using the digit 0-9. (the first digit may be zero) How many such

PINs have repeated digits? (Calculation is necessary to get full credits)

Solution

First we count all possible PINs possible. Ten possible digits on each position

So, 10^4=10000 PINs

Now let\'s count PIN with no repeated digits

10 in first place, then 9 to choose from in second then 8 in third and then 7 in fourth

So, 10*9*8*7=5040

So PINs with repeated digits are:

10000-5040=4960