# How many ways can the captain arrage her schedule?

• MHB
• rainbow1
In summary, there are 2,520 ways the captain can arrange her schedule if she has 5 activities to fit into 7 days. She can arrange her schedule in any order she wants as long as all 5 activities are scheduled within the 7 days. If she only wants to schedule 3 activities, there are 210 ways to arrange her schedule. With 10 activities, there are 5,040 ways to arrange her schedule. Technically, there is no limit to how many activities the captain can schedule in 7 days, but it becomes more difficult to find a feasible and efficient schedule as the number of activities increases.
rainbow1
Captain Jane Way is a charter plane pilot and has trips scheduled to Seattle,Dallas, San Francisco, New York, Portland, Omaha, Miami, Honolulu, Arlington, Los Angeles, and Chicago. How many ways can the captain arrage her schedule?

How many choices does the good Captain have for the first destination on her schedule?

## 1. How many ways can the captain arrange her schedule if she has 5 activities to fit into 7 days?

There are 7*6*5*4*3 = 2,520 ways the captain can arrange her schedule.

## 2. Can the captain arrange her schedule in any order she wants?

Yes, the captain can arrange her schedule in any order she wants as long as all 5 activities are scheduled within the 7 days.

## 3. What if the captain only wants to schedule 3 out of the 5 activities?

If the captain only wants to schedule 3 activities, then there are 7*6*5 = 210 ways to arrange her schedule.

## 4. How many ways can the captain arrange her schedule if she has 10 activities to fit into 7 days?

There are 7*6*5*4*3*2*1 = 5,040 ways the captain can arrange her schedule with 10 activities.

## 5. Is there a limit to how many activities the captain can schedule in 7 days?

Technically, no. However, as the number of activities increases, the number of possible arrangements also increases exponentially, making it more difficult to find a feasible and efficient schedule.