Geraldine is picking a four-digit password by using the digits 0 through 9. she can use each digit only once. how many different passwords are possible?

The number of different passwords possible are:

                    5040

It is given that:

Geraldine is picking a four-digit password by using the digits 0 through 9.

Also she has to use each digit just once.

Hence, the number of such passwords possible are:

            10×9×8×7=5040

( Since for the first place we have 10 choices as any of the digit 0-9 could come.

Also, for the second place we will have 9 choices as the number which came at the first place can't be placed again at the second.

Similarly for the third place we have 8 choices as the number which came in the first and second place is not be repeated

and for the fourth place any of the remaining 7 numbers could come up)