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The number of one-one functions f : {a, b, c, d} → {0, 1, 2, ..., 10} such that 2f(a) - f(b) + 3 f(c) + f(d) = 0 is ______. (in integer)
    Correct answer is '31'. Can you explain this answer?
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    The number of one-one functions f : {a, b, c, d} →{0, 1, 2, ..., ...
    ∵ 3f(c) + 2f(a) + f(d) = f(b)
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    The number of one-one functions f : {a, b, c, d} →{0, 1, 2, ..., ...
    The number of one-one functions f : {a, b, c, d} can be calculated using the principle of permutation.

    Since f is a one-one function, each element in the domain {a, b, c, d} must map to a distinct element in the range.

    For the first element, there are 4 choices of elements in the range to map to.
    For the second element, there are 3 choices remaining.
    For the third element, there are 2 choices remaining.
    For the fourth element, there is only 1 choice remaining.

    Therefore, the total number of one-one functions is 4 * 3 * 2 * 1 = 24.
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