Two wizards try to create a spell using all the four elements, water, air,…
2024
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?
- A.
24
- B.
48
- C.
16
- D.
12
Attempted by 107 students.
Show answer & explanation
Correct answer: A
Answer: Each wizard makes 24 attempts.
Key idea: count all possible orders (permutations) of the four distinct elements because order matters.
First position: 4 choices.
Second position: 3 remaining choices.
Third position: 2 remaining choices.
Fourth position: 1 remaining choice.
Multiply the counts: 4 × 3 × 2 × 1 = 24. Therefore, each wizard tries 24 different orders.
Why the other answer choices are incorrect:
48: This is 2 × 24 and could come from adding both wizards' attempts together. The question asks for attempts per wizard independently, so this is not correct.
16: This equals 4^2 and matches the number of length-2 sequences with repetition, which is not what we need when ordering all four elements.
12: This equals 4 × 3 and counts arrangements for only two positions without repetition (permutations of 2 out of 4), not the full ordering of four items.
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