If a man has the choice of traveling between Hisar and Delhi by 8 trains, in how many possible ways he can complete the return journey, using a different train in each direction?

Question: If a man has the choice of traveling between Hisar and Delhi by 8 trains, in how many possible ways he can complete the return journey, using a different train in each direction?

Solution:

For the outward journey he has the choice of using all the 8 trains. Having completed the outward journey, he will be left with only 7 trains to complete the return journey.
Thus, the total number of ways in which he can complete the journey are 8(8 – 1) = 56.

Some general rules regarding permutation are as follows:

For finding permutation of doing ‘n’ function in ‘r’ ways, the formula is

Prem. = n(n -1) (n – 2) x (n – 3) x (n – 4)….

This formula can also be written as follows:

P = n !*/(n – r) !