Answer to Question #135815 in Discrete Mathematics for Chetan pawar

Question

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

Answer 1

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 = ^aC_r * ^bC_r

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.