There are 4 ways between Delhi and Mumbai. In how many ways can a person comes back after going from Delhi to Mumbai if he returns
(i) with the same way?
(ii) with any way?
(iii) with any remaining way?

Explanation

(i) No. of ways of going from Delhi to Mumbai = 4
No. of ways of coming back from the same way = 1
`:.` From multiplication theorem,
required ways `= 4 xx 1 = 4`.
(ii) No. of ways of going from Delhi to Mumbai = 4 No. of ways of coming back with any way = 4
`:.` From multiplication theorem,
required ways `= 4 xx 4 = 16`
(iii) No. of ways of going from Delhi to Mumbai = 4 No. of ways of coming back with any remaining way = 3
`:.` From multiplication theorem,
required ways `= 4 xx 3 = 12`.