There are four bus routes between A and B and three bus routes between B and C A man - Maths - Permutations and Combinations

Question

There are four bus routes between A and B and three bus routes
between B and C A man can travel round trip in no of ways by bus
from A to C via B and C to A via B If he does not want to use a bus
route more than once, in how many ways can he make round trip?

Ajanta Trivedi · Accepted Answer

since there are 4 bus route from A to
B and 3 routes from B to C
therefore , there are 4*3 = 12 ways from A to C
since it is round trip, therefore man will travel back from C to A
via B
now the man does not want to use the same bus route from C to B and
from B to A
therefore number of ways of coming back from C to B is 2 and from B
to A is 3
therefore , there are 2*3 = 6 ways from C to A [such that no same
route is repeated]
thus there are 12*6 = 72 ways in which he can make a round trip

hope this helps you

There are four bus routes between A and B and three bus routes between B and C. A man can travel round trip in no. of ways by bus from A to C via B and C to A via B. If he does not want to use a bus route more than once, in how many ways can he make round trip?