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    Shift Cipher- No. of non-Fixed Mapping substitution tables possible.


    A substitution table is said to be a fixed mapping if at least one of the characters maps to itself, i.e. A-->A.
    How many substitution tables will be there where not even a single alphabet maps to itself.

    My solution:-

    I first tried to find out number of substitution tables with fixed matching.
    If only 26 alphabet maps to itself- No. of substitution tables with fixed mapping will be 1
    If only 25 alphabets maps to itself- No. of substitution tables with fixed mapping will be 0
    If only 24 alphabets maps to itself- No. of substitution tables with fixed mapping will be (26C2)
    If only 23 alphabets maps to itself- No. of substitution tables with fixed mapping will be (26C3)*2
    If only 22 alphabets maps to itself- No. of substitution tables with fixed mapping will be (26C4)*9
    If only 22 alphabets maps to itself- No. of substitution tables with fixed mapping will be (26C5)*44

    The main problem is that there is not a general formula for calculating no of fixed mapping if we know that a particular no. of alphabets map to themselves.

    If you have any other solution/approach to this problem, please share it.
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    Rewrite your post using more precise definitions.

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