Two wizards try to create a spell using all the four elements: water, air, fire, and earth. For this, they decide to mix...

Question

Two wizards try to create a spell using all the four elements: water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combinations of elements, they conclude that the spell does not work. How many total orders did they together try?

A. 24  B. 48  C. 10  D. 12

Accepted Answer

Together the two wizards tried 24 distinct orders in total. Answer: A. 24. Each wizard mixes all four elements in all possible orders. The number of ways to arrange 4 distinct elements is 4! = 24. Since they work independently and both try ALL possible orders, each wizard tries the same 24 orders. However, the question asks for the total orders they tried together — since they each try the same complete set of 24, the combined total is still 24 distinct orders (no new orders are added by the second wizard). The answer A = 24 confirms this interpretation: they tried 24 distinct orders combined.