Probability of Arranging Rooks on Chessboard with Rook Polynomials

[sam_0017]

help withe this tow Question please ?

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 ?

 

[sam_0017]

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 .