Official Explanation
1. Which of the following is the maximum number of permutations possible for the different schedules that a camper could create for any day spent on the camp premises (Monday, Wednesday, and Friday)?
To answer this question, you must first determine which day would have the most number of possibilities for a camper’s schedule. A quick look at the three days shows that it must be Friday, as that day has an extra activity session at the end of the day AND two of the sessions that day are Camper’s Choice, which have the highest number of possibilities. Using your basic understanding of combinatorics, you need to select the number of possibilities for each session on Friday and then multiply them together.
For the Waterfront Activity there are 3 choices, for the Arts and Crafts Activity there are 3 choices, and for the Team Sports Activity there are 4 choices. So for the first three sessions that day, there are 3 x 3 x 4 or 36 possible permutations.
In the afternoon there are two Camper’s Choice sessions with 13 activity choices for each and one Camping Activity with 3 choices. This means there are 13 x 13 x 3 or 169 x 3 = 507 possible permutations in the afternoon.
The correct answer is thus 36 x 507, which with a quick estimation and look at the units digit must be (D) —18,252.
3. On one of the days spent at camp (Monday, Wednesday, and Friday), a certain camper spends one of his activity sessions participating in Swimming. For each activity listed below, select “Possible” if the camper could have done this activity immediately after Swimming and mark “Not Possible” if the camper could not have done this activity immediately after Swimming.
To answer this question, you must look at all the places on the M/W/F schedule during which a camper could participate in Swimming—that would be any session marked Waterfront Activity or Camper’s Choice.
For Monday, Arts and Crafts falls after Waterfront Activity and Camping Activity falls after Camper’s Choice. So for Monday, only Shelter Building would be possible after Swimming.
On Wednesday, no choice of activities comes after Waterfront Activity and Arts and Crafts comes after Camper’s Choice. Therefore, none of the three given activities are possible after Swimming on Wednesday.
For Friday, Arts and Crafts comes after Waterfront Activity and Camping Activity comes after the first Camper’s Choice. There is no choice of activity after the second Camper’s Choice. So on Friday, only Shelter Building is possible after Swimming, as it is a Camping Activity.
The correct answer is Possible for Shelter Building and Not Possible for Sailing and Basketball.