GATE CS 2024 Set 2 Q.2: Quantitative Aptitude

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?

Official answer and solution

Official answer: A
From: Official GATE 2024 answer key

Solution

Count the number of permutations of 4 distinct elements for a single wizard.

There are $4$ distinct elements (water, air, fire, and earth). The number of ways to mix all $4$ elements in all possible orders is the number of permutations of $4$ distinct items:

4! = 4 \times 3 \times 2 \times 1 = 24

Since the question asks how many attempts each wizard makes independently, each wizard makes $24$ attempts.

Final answer

Option (A)

Common trap

Multiplying by 2 to get 48 (total attempts by both wizards combined) instead of the attempts made by each wizard independently.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2024 Computer Science and Information Technology - Set 2 (CS2)
Question: 2 of 65
Section: General Aptitude

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