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Math Help - Question about factorials (I think)

  1. #1
    Junior Member
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    Question about factorials (I think)

    Im not entire sure how to explain this, but I know what a factorial is and how to use it in a basic sense. I guess you can say the number of variations of abcd is 4*3*2*1=24, right?

    How would I figure out something like this mathematically:

    the number of ways you can use capital and lowercase a's

    aa AA aA Aa

    theres only two variations, a and A. 2*1=2.

    so my logic clearly doesnt work here lol

    Also, how would I figure out something like how many variations are possible with a dataset of 3 members, with the dataset being populated with the possible genders being born

    example:
    b-b-b
    g-g-g
    b-g-g
    b-g-b
    etc

    Im sure I didnt explain this well, and im not even sure if this is the forum it goes to but I would really like an answer to this, because trying to figure out how many variations that can occur the long tedious way is well.... tedious

    thank you for any help
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  2. #2
    MHF Contributor Unknown008's Avatar
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    You're right that this is not the right board, but then, I'm not sure either since one thread similar to this got moved from the simple probability and statistics board, and I do factorials, permutations and combinations in statistics.

    To answer your first question:

    the number of ways you can use capital and lowercase a's

    aa AA aA Aa

    theres only two variations, a and A. 2*1=2.
    Here, there are repeats, and as such, is different. My way of solving this is this:

    I first put two blanks: _ _

    In the first blank, I can have either a or A, so, two possibilities.
    In the second blank, I can get either a or A, so again two possibilities.

    Total becomes 2 x 2 = 4

    This works with more than two items too.

    With abc, you can have:
    aaa, aab, aba, aac, aca, abc, acb, abb, acc,
    baa, bab, bba, bbb, bac, bca, bcc, bcb, bbc
    caa, cab, cba, cbb, cac, cca, ccc, ccb, cbc

    Which is obtained using the logic; 3 possibilities in each blank, hence, 3 x 3 x 3 = 27

    IF there were no repeats, then 2! is the answer for the first case, and 3! for the second case.

    Oh, I see I already answered your next question
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