Question

Answer the questions below.

(a) There are 14 European cities that Kevin would eventually like to visit. On his next vacation, though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.) (b) From the 12 albums released by a musician, the recording company wishes to release 8 in a boxed set. How many different boxed sets are possible?

Answer 1

Answer a:
There are 14 European cities to visit and Kevin has only time to visit 3 of the cities on three different days (Monday, Tuesday and Wednesday)

Now, Kevin has 14 choices to visit a city on Monday, 13 choices for Tuesday and 12 choices for Wednesday

Also, the city he chose to visit on Monday, he could have visited it on Tuesday or Wednesday as well and same goes to the cities he visited on the next days as per his schedule

So, the total number of different possible schedules are 14C3 = 364

Answer b:
There are 12 albums released by a musician and the recording company wishes to release 8 in the boxed set.

Therefore, total number of different boxed set possible are 12C8 = 495 (Since, one has to choose 8 from 12 at a time)