Title: CAT 2020 Quant Slot 3 - Indian Game Problem Solution
Problem Statement (Assumed Based on Common CAT Themes):
In a traditional Indian game, players arrange 5 distinct stones (R, B, G, Y, P) in a line. No two adjacent stones can share the same color. How many valid arrangements are possible?
Solution:
First Stone:
There are 5 choices (R, B, G, Y, P).
Subsequent Stones (2nd to 5th):
Each subsequent stone must differ from its predecessor. For each position after the first, there are 4 valid choices (excluding the color of the previous stone).
Total Arrangements:
Multiply the choices for each position:
[
5 \times 4 \times 4 \times 4 \times 4 = 5 \times 4^4 = 5 \times 256 = 1280
]
Answer:
\boxed{1280}
Key Takeaways:
Permutations with Restrictions: When adjacent elements cannot repeat, use a chain multiplication approach.
CAT Strategy: For slot-based exams, practice quick calculations and recognize pattern-based problems (e.g., color/arrangement constraints).
Note: This solution assumes a common CAT problem type. For precise answers, provide the exact question statement.
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