Duke Maverick worked for a packaging company. One Day, Duke received four separate orders and acidentally mixed up the addresses, so he applied the address labels at random, what is the probability that exactly three packages were correctly labeled?

If three were labeled correctly, so was the fourth, since the remaining one would have to match.
The chances of getting the first label correct are 1/4. For the next, it is 1/3 and the third, it is 1/2. The overall probability is the product,
P = (1/4)*(1/3)*(1/2) = 1/24

I would not have concluded that. But it makes sense. Brilliant.

The probability that exactly three packages were correctly labeled is 1/24.

To find the probability that exactly three packages were correctly labeled, we can use the principle of independent events.

First, we need to determine the number of ways to arrange the four packages. Since Duke randomly applied the labels, there are 4! (4 factorial) ways to arrange the labels.

Next, we need to determine the number of ways to choose three packages to be labeled correctly. The number of ways to choose 3 packages out of 4 is given by the binomial coefficient, also known as "4 choose 3" or C(4, 3), which can be calculated as 4!/[(3!)(4-3)!] = 4.

Therefore, the total number of favorable outcomes (three packages labeled correctly) is 4.

Finally, the probability of exactly three packages being labeled correctly is given by dividing the favorable outcomes by the total number of possible outcomes:

Probability = Favorable Outcomes / Total Outcomes

Probability = 4 / (4!) = 4 / (4*3*2*1) = 4 / 24 = 1/6

So, the probability that exactly three packages were correctly labeled is 1/6.