High School Statistics Problem 12 (Awarding B.A.)?

How many 4 digit pins can be made with the numbers "121234"?

4 Answers

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  • 2 months ago
    Best Answer

    Taking what Leonard started, I am thinking that the digits can't be reused, but since there are duplicate numbers, his count of 360 possible outcomes includes duplicates:

    1234 (using the first 1 and first 2)

    1234 (using the first 1 and second 2)

    1234 (using the second 1 and first 2)

    1234 (using the second 1 and second 2)

    It should still count as 1 occurrence instead of 4.

    To get rid of the duplicates, since there are 2 1's and 2 2's, you divide the number of possible outcomes by (n!) for each. Since it's 2 each, divide by (2! * 2!) which is 4, so:

    360 / 4 = 90 unique 4-digit PINs using the 6 digits shown.

  • 2 months ago

    The actual answer is 102 as I explained in the follow-up version. The digits were all reduced by 1, but it doesn't change the number of PINs. See the link below:

  • Anonymous
    2 months ago

    Combinations with repetition

    1 2 1 2 3 4 - 6 elements where 1 and 2 are repeated

    CR (n, r) = (n + r - 1)! / (r! (n-1)!)

    n = 6, r = 4

    CR (6, 4) = (6 + 4 - 1)! / (4!.* 5!)

    CR (6, 4) = 9! / (5(4!)²)

    CR (6, 4) = 126

  • 2 months ago

    Your question is very unclear - can you reuse the digits? e.g, 1111?

    if yes, then there are 4 unique digits, and there are 4 choices for each of the places for the 4-digit pin, so 4^4=256.

    if you are supposed to think of your "121234" as 6 choices which cant be reused, then there are 6 choices for the 1st digit, 5 choices for the 2nd, ...., and then there would be 6x5x4x3=360 possibilities.

    Or the question could be asking something else - who knows.

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