A randomly generated password has four characters. Each character is either A, B, C, D, E or F or a number from 0 – 9. Each character

Question

A randomly generated password has four characters. Each character is either A, B, C, D, E or F or a number from 0 –
9. Each character in the password can only be used once. What is the probability that a password has only one
number?

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Athena 4 weeks 2021-09-17T15:02:38+00:00 1 Answer 0

Answers ( )

  1. Emma
    0
    2021-09-17T15:04:02+00:00

    44%

    Sample space is 36C4

    Now, we want to know all of the combinations that have 1 digit in it.

    So, we can have one here:

    1XXX

    X1XX

    XX1X

    XXX1

    But we have 10 different digits to choose from. So, we need to introduce the combination term, nCr, where n is a list of all digits and r is how many we want.

    Since we only want one, we will need 10C1 for the number of digits. But we need to choose three lowercases, so it becomes 10C1 × 26C3

    Since it’s a probability question, we need to divide that by our sample space, 36C4, and our percentage becomes 44%

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45:7+7-4:2-5:5*4+35:2 =? ( )