# Question: you choose a random permutation p1 p2 p3 p4 p5...

###### Question details

You choose a random permutation (p1, p2, p3, p4, p5, p6, p7) of 1, 2, 3, 4, 5, 6, 7, with each of the 7! permutations equally likely. What is the probability that

(1 + p1)(2 + p2)(3 + p3)(4 + p4)(5 + p5)(6 + p6)(7 + p7)

is even? Give an exact answer as a simplified fraction and justify your answer.