Final answer:
There are 24 different ways to arrange 4 window displays in 4 different display cases, calculated by the factorial of 4 (4!).
Step-by-step explanation:
The question asks how many different options there are for arranging the 4 window displays in the 4 different display cases. This is a problem that involves permutations since we are concerned with the order of the displays.
The number of different arrangements (permutations) of the 4 displays is given by 4! (four-factorial), which equals 4×3×2×1. Therefore, there are 24 different ways to arrange the displays. This factorial calculation accounts for all the possible ways in which the displays can be arranged in an orderly manner, considering each display is unique.
It might be helpful to write out all 24 combinations to understand how the arrangements work and to get practice in systematizing the combinations. The systematic approach allows you to verify why 4×3×2×1 correctly counts all the permutations.