## Thinking Mathematically (6th Edition)

Of the 7 places on the bench, places 4 and 5 are taken by the counselor and the troublesome camper. So, there are 5 places to be filled by 5 remaining campers. 1. The camper for the 1st place can be chosen in 5 ways. 2. The camper for the 2nd place can be chosen in 4 ways. 3. The camper for the 3rd place can be chosen in 3 ways. 4. The camper for the 4th place can be chosen in 2 ways. 5. The camper for the 5th place can be chosen in 1 ways. The total number of arrangements is $5\times 4\times 3\times 2\times 1=120$