In how many ways can 4 different colored balls be placed in 3 different boxes?

In how many ways can 4 different colored balls be placed in 3 different boxes?

Step 1: Identify the number of balls. We have 4 different colored balls.
Step 2: Identify the number of boxes. We have 3 different boxes.
Step 3: Understand that each ball can be placed in any of the 3 boxes. This means for each ball, there are 3 choices.
Step 4: Since there are 4 balls and each ball has 3 choices, we multiply the choices together. This is done by raising the number of choices (3) to the power of the number of balls (4).
Step 5: Calculate 3 raised to the power of 4, which is 3^4.
Step 6: Perform the calculation: 3^4 = 3 * 3 * 3 * 3 = 81.
Step 7: Conclude that there are 81 different ways to place the 4 different colored balls into the 3 different boxes.

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