Question

Four trumpet players’ instruments are mixed up, and the trumpets are given to the players just before a concert. What is the probability that no one gets his or her trumpet back?
A. 3/8
B. 3/4
C. 1/2

Answer 1

This is what is known as a derangement - an arrangement in which none of the objects maintain their original position.
For example, with the numbers, 1234, in how many ways can they be arranged so that 1 is NOT in first position, 2 is NOT in second position, etc.
Of the 24 possible permutations of four numbers, there are nine possible derangements:
2143   2341   2413
3142   3412   3421
4123   4312   4321
So, the probability that no one gets their own trumpet is
9 out of 24 = 3/8  answer is A
Source:
http://www.1728.org/derange.htm