Topic
Class 10A students plan to travel to only one of two cities, city M or city N. Since going during the day, you need to make a list of 4 places to visit and the order to go to those places from prior to. Knowing that, you list out 10 places you can go in city M and 4 places you can go in city N. How many ways can Class 10A students make a list of places to travel?
Solution method – See details
Apply the rules of addition, permutation, and union
Step 1: Calculate the number of ways to choose 4 places to visit in city M (in order)
Step 2: Calculate the number of ways to choose 4 places to visit in city N (in order)
Step 3: Apply the addition rule to find the number of satisfying choices
Detailed explanation
Case 1: Class 10A goes to M city.
Each way of choosing and ordering 4 places to visit if class 10A goes to city M is a convolution of 4 of 10.
The number of ways to choose and order 4 places to visit if class 10A goes to city M is: \(A_{10}^4 = 5040\) how to choose
Case 2: Class 10A goes to city N.
Since city N has only 4 places to visit, each placement order for those 4 places is a permutation of 4 elements.
The number of ways to order 4 places to visit is: \({P_4} = 4! = 24\) ways to choose
According to the rule of addition, class 10A has a total of 5 040 + 24 = 5 064 ways to make a list of places to visit.
