Solution: 2017 Winter Final - 17
Author: Michiel SmidQuestion
Consider a uniformly random permutation of the set $\{1,2,\dots,50\}$. Define the event
- A = "in the permutation, both 8 and 4 are to the left of both 1 and 2".
(a)
1/6
(b)
1/5
(c)
1/3
(d)
2/3
Solution
For all intents and purposes, the set we really care about is $ |S| = 4! $
We can do $ { (1,2), (2,1) } $ on the left side: 2
We can do $ { (8,4), (4,8) } $ on the right side: 2
$ |A| = 2 \cdot 2 $
$ Pr(A) = \frac{4}{24} = \frac{1}{6} $