Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3, ..., 20. What is the probability that 2 appears at an earlier position than any other even number in the selected permutation? A. 1/2 B. 1/10 C. 9!/20! D. None of these

GATE 2007 · Engineering Mathematics · Uniform Distribution · easy

Answer: P(2 appears before all other even numbers) = 1/10. Answer: B.

1. Identify the even numbers: There are exactly 10 even numbers among 1 to 20.
2. Apply symmetry: each even is equally likely to be first: By symmetry of uniform random permutations, each of the 10 even numbers is equally likely to appear first among them. So P(2 first) = 1/10.