Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
There are 4 hotels in a town. If 3 men check into the hotels in a day then the probability that each checks into a different hotel is
MathematicsProbabilityAP EAMCETAP EAMCET 2022 (05 Jul Shift 2)
Options:
  • A $\frac{6}{7}$
  • B $\frac{1}{8}$
  • C $\frac{3}{8}$
  • D $\frac{5}{9}$
Solution:
1767 Upvotes Verified Answer
The correct answer is: $\frac{3}{8}$
Total number of ways in which 3 men can check in 4 hotels $=4 \times 4 \times 4=64$
If each men has to check in different hotel,
no. of ways ${ }^4 \mathrm{C}_1 \times{ }^3 \mathrm{C}_1 \times{ }^2 \mathrm{C}_1$
$=4 \times 3 \times 2=24$
( 4 choices for 1 st men, 3 for 2 nd and 2 for 3 rd)
Required probability $=\frac{24}{64}=\frac{3}{8}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.