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Rook polynomials

  1. Oct 16, 2011 #1
    help withe this tow Question plz ?

    Q1:

    A pair of dice, one red and the other green, is rolled six
    times. We know that the ordered pairs (1, 1), (1, 5), (2, 4),
    (3, 6), (4, 2), (4, 4), (5, 1), and (5, 5) did not come up. What is
    the probability that every value came up on both the red die
    and the green one?

    ======================================================
    Q2:

    Let C be a chessboard that has m rows and n columns,
    with m ≤ n (for a total of mn squares). For 0 ≤ k ≤ m, in
    how many ways can we arrange k (identical) nontaking
    rooks on C ?
     
  2. jcsd
  3. Oct 16, 2011 #2
    and also this question ?

    For A = {1, 2, 3, 4, 5} and B = {w, v, w, x, y, z], deter-
    mine the number of one-to-one functions f:A→B where
    f(1)≠v or w , f(2)≠u or w , f(3)≠x and f(4)≠v or x or y .
     
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