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Combination of r Things from n Things When All Are Not Different

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Question

There are $2$ gates to enter a school and $3$ staricase from first floor to the second floor. How many possible ways are there for a student to go from outside the school to a classroom on the second floor and come back?

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Solution

Total choices for the student to up cards journey $= 2 \times 3 = 6$
Similarly for downwards journey $= 6$
$\Rightarrow$ Total choices $= 6 \times 6 = 36$

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Combination of r Things from n Things When All Are Not Different

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