Final answer:
To distribute 5 shirts among 3 persons so that each person gets at least one shirt, we can use permutations. The total number of ways is 45.
Step-by-step explanation:
To find the total number of ways in which 5 shirts of different colors can be distributed among 3 persons so that each person gets at least one shirt, we can solve this using the concept of permutations.
First, we distribute one shirt to each person, which leaves us with 2 shirts and 3 persons. The remaining 2 shirts can be distributed among the 3 persons in 3! (3 factorial) ways. For each of these ways, the first person can get one of the 2 shirts, and the remaining 2 persons can each get one of the 2 shirts. So, the total number of ways is 3! * 2 * 2 = 12 * 2 * 2 = 48.
However, we also need to consider the case where one person gets all the remaining 2 shirts. There are 3 ways this can happen. So, we need to subtract these 3 cases from the total. The final answer is 48 - 3 = 45.