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:

For problems involving arrangements, remember to calculate the number of permutations using ( n! ), where ( n ) is the total number of items to arrange.

Answer 1

The Correct Option is A

Step 1: Total permutations of the elements.
There are four elements: water, air, fire, and earth. The total number of ways to arrange these elements in all possible orders is given by the factorial of the number of elements: [ 4! = 4 times 3 times 2 times 1 = 24 ] 
Step 2: Independent attempts.
Each wizard works independently, and both attempt all the possible arrangements of the four elements. Thus, each wizard makes (24) attempts before concluding that the spell does not work.
Step 3: Verifying the correct option.
Since (4!) equals (24), the correct answer is (A) 24.