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Thread: Combinations/Permutations where only certain elements in series can vary

  1. #1

    Combinations/Permutations where only certain elements in series can vary

    Hi all,

    I am sorry if this is posted the wrong sub-forum, but my math knowledge is limited and so I am unsure where else to post.

    I am wondering how to calculate the number of possible versions of a series of characters, where only some characters in the series can vary.

    5NMB RTTM 8L60 9P7U AJQW 9889

    5 N M B R T T M 8 L 6 0 9 P 7 U A J Q W 9 8 8 9
    L

    N

    G O

    4

    3
    V
    B B


    How many different combinations are possible where only bold characters can vary and they can vary only with the character directly beneath them in the table? Is there a formula for this?

    Therefore, the following are possible (characters in red are variations on the original series):

    5NMB LTTM 8L60 9P4U AJQW 9889

    5NMB RTTM 8L60 9P7U AJQW 9BB9

    5NMB LTTN 8LGO 9P4U A3QV 9889

    But the following is NOT:

    5NMB NTTO 8L60 9P7U ABQB 93V9

    I hope this makes sense, and I hope it is ok to post here. I am new to the forum so forgive me if my posting etiquette or anything is off-point.

    I look forward to your responses.

  2. #2
    Senior Member
    Join Date
    Sep 2012
    Posts
    2,486
    If I understand the problem, you have a sequence of characters. At specific spots in the sequence, a character may be replaced by one other character.

    You have 9 spots where an alternative is permitted.

    So the number of possible different sequences is [tex]2^9 = 512.[/tex]

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