GRE Exam Numerical Ability Permutation and Combination

At a banquet, 9 women and 6 men are to be seated in a row of 15 chairs. If the entire seating arrangement is to be chosen at random, what is the probability that all of the men will be seated next to each other in 6 consecutive positions?
(A) 1/(15/6)
(B) 6!/(15/6)
(C) 10!/15!
(D) 6! 9! /14!
(E) 6! 10! / 15!

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GRE Other Question

The minimal distance between any point on the sphere (x-2)^2 + (y-1)^2 + (z-3)^2 = 1 and any point on the sphere (x+3)^2 + (y-2)^2 + (z-4)^2 = 4 is
(A) 0
(B) 4
(C) Sqrt(27)
(D) 2(Sqrt2 + 1)
(E)3(Sqrt3 – 1) Let M be a 5*5 real matrix. Exactly four of the following five conditions on M are equivalent to each other. Which of the five conditions is equivalent to NONE of the other four?
(A) For any two distinct column vectors u and v of M, the set {u, v} is linearly independent.
(B) The homogeneous system Mx = 0 has only the trivial solution.
(C) The system of equations M x = b has a unique solution for each real 5*1 column vector b.
(D) The determinant of M is nonzero.
(E) There exists a 5*5 real matrix N such that NM is the 5*5 identity matrix.