To access his bank’s atm, tom must choose a four-digit pin. any digit from 0 through 9 can be used in the pin, but digits may not be repeated. how many possible pin numbers are there?

The first digit can be any one of the 10 available digits.
. . . For each one . . .
The second digit can be any one of the 9 unused others.
. . . For each one . . .
The third digit can be any one of the 8 unused others.
. . . For each one . . .
The fourth digit can be any one of the 7 unused other.

So the total number of possible choices is

(10 x 9 x 8 x 7) = 5,040 possible PINs