Question

Byron bought a keyless entry door lock that has the digits 0 through 9 on the keypad. He wants to choose a three-digit entry code. How many different combinations are possible, if the digits can be repeated? 27 30 729 1,000

Answer 1

Let the combination be of the form XXX
So, we have 3 digits in our combination, with repetition allowed
So, to type in 1st digit X, we have 10 options i.e. 0 to 9
Similarly, to type in 2nd digit, we have 10 options i.e. 0 to 9
Again, to type in 3rd digit, we have 10 options i.e. 0 to 9
So, for typing the XXX combination, no. of ways possible will be given by=
(10) x (10) x (10) = 1000

Therefore, he can type the combination in 1000 ways.