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?
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Answer: A
To find the number of attempts made by each wizard independently, we need to calculate the number of possible orders in which the four elements can be mixed.
The four distinct elements are:
- Water
- Air
- Fire
- Earth
Since all four elements must be used in each attempt, and the order of mixing matters (i.e., "all possible orders"), this is a permutation problem of arranging distinct items.
The number of possible permutations of distinct elements is given by:
Since each wizard works independently and tries all possible combinations, each wizard makes exactly attempts.
Therefore, the correct option is A.
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