Answer:
This is a permutation problem because the order of their choice is important.
There are 210 ways in which this choice can be made.
Step-by-step explanation:
Complete Correct Question
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities. Cody and Aaliyah are planning trips to two countries this year. There are 15 countries they would be interested in visiting. One trip will be one week long and the other two weeks.
Solution
Permutation is used to calculate the number of possibilities or number of ways k choices can be made from n options given that the order of picking the choices is important. If there are choices A, B and C, picking ABC is different from CAB if order of picking is important like permutation preaches.
Combination on the other hand, is used to calculate the number of possibilities or number of ways k choices can be made from n options given that the order of picking the choices is unimportant. If there are choices A, B and C, picking ABC is the same as picking CAB if order of picking is unimportant like combination preaches.
So, in this question, Cody and Aaliyah want to pick 2 countries to visit, out of 15. They plan to spend 2 weeks in one country and 1 week in the other country.
This last sentence makes the order in which they pick the countries to visit important. If they chose to spend two weeks in country A and one week in country B, it is now a different possibility from spending two weeks in country B and one week in country A.
Hence, this is a permutation problem
The number of possibilities of picking 2 countries out of 15 countries to spend 2 weeks in first country and spend 1 week in the other country is ¹⁵P₂ = 15! ÷ (15 - 2)!
= 210 ways in which this choice can be made.
Hope this Helps!!!
