Question

After school(S), Feroz can either go to circus(C) or to a movie theatre(T), after which he goes home. The ways in which he can go from one place to other are given as paths shown. The number of ways Feroz can go from School to Home is given by

• A. 12
• B. 2
• C. 10
• D. 14

Answer 1

The correct option is D

14

The possible ways in which Feroz can go from school to home are

i.) School$\to$Theatre$\to$Home i.e., School to Theatre AND Theatre to Home

(OR)

ii.) School$\to$Circus$\to$Home i.e., School to Circus AND Circus to Home

By Fundamental principle of counting, number of ways Feroz can reach home from school is given by replacing AND with x and OR with + in the above statements.

i.) Paths for School$\to$Theatre$\to$Home can be taken in $3\times 4$ = 12 ways

ii.) Paths for School$\to$Circus$\to$Home can be taken in $2\times 1$ = 2 ways

So the total number of ways of reaching home are 12+2 = 14 ways