Solution to There are 6 routes from Delhi to Mumbai and 12 routes from Mumbai to Bangalore. … - Sikademy
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Archangel Macsika

There are 6 routes from Delhi to Mumbai and 12 routes from Mumbai to Bangalore. In how many ways can you travel from Delhi to Bangalore via Mumbai? 18 72 36 16

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Here's the Solution to this Question

Given that,


Number of routes from Delhi to Mumbai a = 6

Number of routes from Mumbai to Bangalore b = 12


Hence the total number of routes from Delhi to Bangalore via Mumbai is given by c = aCr * bCr


Since one can travel in any 1 way only hence r = 1 in both the cases


\therefore c = \frac {a!}{(a-r)!*r!} *\frac {b!}{(b-r)!*r!} = \frac {6!}{(6-1)!*1!}*\frac {12!}{(12-1)!*1!} = 72


Hence we can travel in 72 different ways from Delhi to Bangalore via Mumbai.


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