Chapter 13.8, Problem 2CYP

To determine

To identify:The number of ways can get from outside the school to her locker.

Answer to Problem 2CYP

Total number of ways Shelly get to her locker is $48$ .

Explanation of Solution

Given:

Shelly can enter the school through 4 different doors. Once inside, she can go to her locker using 4 different sets of stairs and then 3 different hallways.

Concept used:

A work of 3 stages can be completed in total number of ways ( TW ) given by $TW=l\times m\times n$ , where l , m , n are number of ways for used to complete first, second and third stage respectively.

Calculations:

Shelly can enter the school through 4 different doors. Once inside, she can go to her locker using 4 different sets of stairs and then 3 different hallways.

The process of reaching the locker entering through one door is shown in figure here.

Once entered the school through she can choose 4 stairs and 3 hall ways.

So number of ways to reach locker once entered the school is $4\times 3$ .

Since, there are 4 doors, so total number of ways to get the locker is

  $4\times 4\times 3=48$ .

Thus, total number of ways Shelly get to her locker is

  $TW=l\times m\times n=4\times 4\times 3=48$

Conclusion:

Total number of ways Shelly get to her locker is $48$ .