Question:
There are 4 hotels in a town. If 3 men check into the hotels in a day, what is the probability that each checks into a different hotel?
There are 4 hotels in a town. If 3 men check into the hotels in a day, what is the probability that each checks into a different hotel?
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When individuals are assigned uniquely to categories, use permutations. Divide by total possible assignments.
Updated On: May 17, 2025
- \( \frac{6}{7} \)
- \( \frac{1}{8} \)
- \( \frac{3}{8} \)
- \( \frac{5}{9} \)
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The Correct Option is C
Solution and Explanation
Total number of ways 3 men can choose hotels (each has 4 options):
\[
4^3 = 64
\]
Number of favorable ways where all 3 choose different hotels:
\[
^4P_3 = 4 \cdot 3 \cdot 2 = 24
\Rightarrow \text{Probability} = \frac{24}{64} = \frac{3}{8}
\]
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