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 attempts does each wizard make before coming to this conclusion, independently?

• A. 24
• B. 48
• C. 16
• D. 12

Hint:

The number of arrangements (permutations) of \(n\) elements is always \(n!\). Use this for questions involving ordering.

Answer 1

The Correct Option is A

The total number of possible orders for \(n\) elements is given by the factorial of \(n\), denoted by \(n!\). Step 1: Calculate the number of orders for 4 elements.
The number of permutations of 4 elements is: \[ 4! = 4 \times 3 \times 2 \times 1 = 24. \] Step 2: Verify independent attempts.
Since both wizards work independently and test all possible permutations, each wizard makes \(24\) attempts. Final Answer: \[ \boxed{24} \]