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Question

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


A
30
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B
45
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C
120
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D
60
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Solution

The correct option is D $$60$$
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 $$ = 5 \times 4 \times 3 = 60 $$ ways

Mathematics

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