Question

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 counselor’s immediate right?
there are \\(\square\\) way(s) this can be done.

Explanation:

Step1: Determine the number of fixed - position people

The counselor is fixed in the seventh seat and the trouble - making camper is fixed in the eighth seat. So we only need to arrange the remaining \(8 - 2=6\) campers.

Step2: Use the permutation formula

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 6\). The formula for permutations \(P(n,r)=\frac{n!}{(n - r)!}\), when \(n=r\), \(P(n,n)=n!\). So the number of arrangements of \(6\) campers is \(6!\)

$$6! = 6\times5\times4\times3\times2\times1=720$$

Answer:

\(720\)