Question

how many ways can 5 letters be sent to 3 different boxes

Answer 1

243

Answer 2

We have 5 distinct letters and 3 distinct boxes. For each letter, there are 3 independent choices of boxes it can be sent to. Applying the fundamental principle of counting, the total number of ways is the product of the number of choices for each letter. This results in 3 * 3 * 3 * 3 * 3 = 3^5 = 243 ways.