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)
Explanation
Each attempt is one order in which the four elements are mixed, with all four used every time. The number of orders of 4 different elements is
\[4! = 4 \times 3 \times 2 \times 1 = 24.\]
The wizards work independently, so each one goes through all 24 orders separately. Adding the two wizards’ attempts (48) answers a different question: the total number of attempts, not the number each wizard makes.
Answer: A