A camp counselor and eight campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the seventh seat and a camper who has a tendency to engage in food fights must sit to the counselors immediate right?
We first consider the total number of possibilities without any restrictions. There are 9 choices for who sits in the first seat, 8 choices for the second seat, 7 choices for the third seat, and so on until we get to 2 choices for the sixth seat (since the counselor sits in the seventh seat). Thus, there are $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 2 = 60,\!480$ total possibilities.
Now, we consider the number of possibilities if a camper who has a tendency to engage in food fights sits immediately to the right of the counselor. There are 8 choices for this particular camper (since he cannot sit in the seventh seat, which is reserved for the counselor), and for each such choice there are $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 = 5,\!040$ possibilities for the rest of the campers. This gives a total of $8 \cdot 5,\!040 = 40,\!320$ possibilities where the given camper sits immediately to the right of the counselor.
Therefore, the number of possible seatings where the counselor sits in the seventh seat and a camper who has a tendency to engage in food fights sits immediately to the right of the counselor is $\dfrac{40,\!320}{60,\!480} = \boxed{\dfrac{2}{3}}$.