Really basic probability question that I want answered,
There is a class room with 3 students and 3 seats. Each student selects a seat and sits on it. The next day, the instructor randomly picks a seat for each student. What is the probability that each student is assigned a different seat from the one they sat on yesterday? (i.e: Everyone is in a different seat).
The way I approached the problem was to find the probability of the students sitting in the same seat. If there are 3 students, A, B, C, and the instructor is assigning them to the seats one by one, then
P(A is assigned a different seat than yesterday) = 2/3
P(B is assigned a different seat than yesterday) = 1/2
P(C is assigned a different seat than yesterday) = 1
P(Everyone is assigned a different seat) = 2/3 * 1/2 * 1 = 1/3
Is this the correct way of doing this?