def nth_combination(iterable, r, index):
    """Equivalent to ``list(combinations(iterable, r))[index]``.

    The subsequences of *iterable* that are of length *r* can be ordered
    lexicographically. :func:`nth_combination` computes the subsequence at
    sort position *index* directly, without computing the previous
    subsequences.

    """
    pool = tuple(iterable)
    n = len(pool)
    if (r < 0) or (r > n):
        raise ValueError

    c = 1
    k = min(r, n - r)
    for i in range(1, k + 1):
        c = c * (n - k + i) // i

    if index < 0:
        index += c

    if (index < 0) or (index >= c):
        raise IndexError

    result = []
    while r:
        c, n, r = c * r // n, n - 1, r - 1
        while index >= c:
            index -= c
            c, n = c * (n - r) // n, n - 1
        result.append(pool[-1 - n])

    return tuple(result)