A certain ATM code is required to consist of 4 distinct digi

A certain ATM code is required to consist of 4 distinct digits (0 to 9). If the ATM machine will allow only 3 guesses per day, then how many days would it take to try all possible ATM codes?

Solution

Number of ways to select first digit=10 i.e (0-9)

Number of ways to select second digit= 9 i.e (0-9 except the digits used at first position)

Number of ways to select third digit=8 i.e (0-9 except the two digits used at first & second position)

Number of ways to select fourth digit=7 i.e. (0-9 except the digits used at first,second & third position)

Total number of ATM code=10*9*8*7=5040

Guesses per day =3

Number of days would it take to try all possible ATM codes=5040/3

= 1680