Correct : a

Explanation:
To find the number of trials each wizard makes, we need to calculate the total number of unique ways to arrange the four elements.
1. Identify the Permutation Problem:
• There are 4 distinct elements available: {water, air, fire, earth}.
• The problem states that they mix all four elements in all possible orders.
• Since the order of mixing matters and all items are used without repetition, this is a standard permutation problem of $n$ distinct objects.

2. Calculate the Total Combinations ($n!$):
The number of unique ways to arrange $n$ distinct objects is given by $n$ factorial ($n!$):
• For 4 elements: 4! = 4 × 3 × 2 × 1 = 24.

3. Evaluate per Wizard:
• The question asks for the number of trials each wizard makes before coming to the conclusion.
• Since they work independently and both try all possible combinations, each wizard completes the full set of 24 unique arrangements.

4. Conclusion:
Each wizard makes exactly 24 trials, making option (a) the correct choice.