Multiple choice

Four different items have to be placed in three different boxes. In how many ways can it be done such that any box can have any number of items?

  1. $3^4$
  2. $4^3$
  3. $^4P_3$
  4. $^4C_3$
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A Correct answer
Explanation

Each of the 4 items has 3 choices of boxes. Since the items are distinct and boxes are distinct, the total ways = 3 * 3 * 3 * 3 = 3^4.

AI explanation

Placing 4 different items into 3 different boxes is an application of the fundamental principle of counting, where each distinct item has 3 independent choices of boxes. Multiplying the choices for all items gives 3 multiplied four times (3 * 3 * 3 * 3). This results in 3^4 ways.

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