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Fundamental Principle of Counting

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Question

There are $8$ buses running from Kota to Jaipur and $10$ buses running from Jaipur to Delhi. In how many ways a person can travel from Kota to Delhi via Jaipur by bus $?$

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Solution

Let $E_{1}$ be the event of travelling from Kota to Jaipur & $E_{2}$ be the event of travelling from Jaipur to Delhi by the person.
$E_{1}$ can happen in $8$ ways and $E_{2}$ can happen in $10$ ways.
Since both the events Eand Eare to be happened in order, simultaneously, the number of ways $= 8 \times 10 = 80.$

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