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GATE CS 2024 Set 2 — Question 2

MCQ+1 / -0.33EasyPermutations & CombinationsQuantitative AptitudeGeneral Aptitude

General Aptitude → Quantitative Aptitude → Permutations & Combinations

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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 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

Correct answer

(A) 24

Solution

The problem states that the wizards mix all four elements (water, air, fire, earth) in all possible orders. This implies finding the number of permutations of 4 distinct items.
The number of permutations of nn distinct items is given by n!n!.
Here, n=4n = 4.4!=4×3×2×1=244! = 4 \times 3 \times 2 \times 1 = 24Since each wizard works independently and tries all possible orders, each wizard makes 24 attempts.

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