You are assigned a computer generated 4-digit password to access your new voice mail account. If the

digits can not be repeated, how many passwords are possible?

b

34 different passwords are possible

5,040 different passwords are possible

40 different passwords are possible

10,000 different passwords are possible

d

5,040 different passwords are possible

Step-by-step explanation:

Assuming that 4-digit means using only numeric values.

This is a permutations problem.

n = number of values used with number values only this is 10

r = the number used in each case without repeating in this case 4

nPr = n! / (n - r) !

nPr = 10! / (10-4) !

nPr = 10! / 6!

The! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24

A quick hack for dividing factorials is to use cancelling.

10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)

= 5040