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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
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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 $=\frac{24}{64}=\frac{3}{8}$
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 $=\frac{24}{64}=\frac{3}{8}$
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