Three persons entered a railway compartment in which 5 seats were vacant. Find the number of ways in which they can be seated?

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30

45

120

60

answer is D.

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Detailed Solution

The number of people and the open seats where they can be seated have been provided to us. Using the idea of permutation and combination, we can determine how many different ways there are to do this.
Combination is calculated using the formula

rnC = \frac{n!}{r! (n - r)!}

where n is the total number of items and n is the number of items that need to be chosen.
We use the product of numbers from that number to

1

to calculate factorial.
The first person can choose to sit in any of the 5 seats in 5 ways.

Then the second person can choose to sit in any of the remaining 4 seats in 4 ways.

Lastly, the third person can choose to sit in any of the remaining 3 seats in 3 ways.

So, total number of ways =5×4×3=60 ways
Hence option (4) is correct.

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