Discussion
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 combination of elements, they conclude that the spell does not work.
How many attempts does each wizard make before coming to this conclusion, independently?
Answer: A
Each wizard makes 24 attempts.
Mixing all four elements in every possible order means trying every arrangement of 4 distinct items, which is
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]
The wizards work independently, so each one tries all 24 orders himself; the count is per wizard, not for the pair.
48 is the total for both wizards together, which the question does not ask for. 16 (\(4^{2}\) or \(2^{4}\)) and 12 (\(4 \times 3\)) do not count the orderings of four elements.
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