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21 January, 05:19

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

+4
Answers (1)
  1. 21 January, 05:28
    0
    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
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