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?

Answer 1

The fundamental principle of counting states that if there are $a$ ways of doing something and $b$ ways of doing another thing, then the total number of ways of doing both things simultaneously are $a \times b.$

Complete step-by-step answer:
It is given that,
There are 8 buses running from Kota to Jaipur
$\Rightarrow$ Number of ways in which a person can travel from Kota to Jaipur by bus = $^8{C_1}$
And there are 10 buses running from Jaipur to Delhi
$\Rightarrow$ Number of ways in which a person can travel from Jaipur to Delhi by bus = $^{10}{C_1}$
Hence by fundamental principle of counting,
Total number of ways in which a person can travel from Kota to Delhi via Jaipur by bus= $^8{C_1}\times ^{10}{C_1}$
Total number of ways in which a person can travel from Kota to Delhi via Jaipur by bus= $8 \times 10 = 80$

Note: For such types of questions we must visualize the scenario and then proceed accordingly as in this question. Counting Principle is the guiding rule for finding the number of ways to accomplish two tasks.