Question

Your television remote control has buttons for digits 0-9. If your press two buttons, how many numbers are possible if

a) the same button may be pressed twice
b) the same button may not be pressed twice​

Answer 1

(A) I got 10(10)=100 points in remote space.

(B) I also got 10(9)=90 points in remote space

Answer 2

a) 100

b) 90

Explanation:

For the first question, the first button you press will have 10 possibilities, from 0-9. For the second button, you will still have 10 possibilities since the same button may be pressed twice. Therefore, you get 10*10=100.

For the second one, the same button may not be pressed twice. For the first button press, you have 10 possibilities, but for the second button, you have 1 less possibility since you aren't allowed to push the button you pressed before. So there will be 9 possibilities. 10*9=90.