Answer
a)10
b)$\frac{n\cdot(n-1)}{2}.$
c)24
d)(n-1)!
Work Step by Step
a)Because the order is not important, we can use the combination rule to determine the number of possibilities: $\frac{5!}{(5-2)!2!}=10.$
b)Because the order is not important, we can use the combination rule to determine the number of possibilities: $\frac{n!}{(n-2)!2!}=\frac{n\cdot(n-1)}{2}.$
c) We can use the factorial rule to determine possbilities for a straight table:$5!=120.$ But at a round table every arrangement is equal to 4 other, hence we have to divide this by 5, hence we get 24.
d) We can use the factorial rule to determine possbilities for a straight table:n! But at a round table every arrangement is equal to (n-1) other, hence we have to divide this by n, hence we get $\frac{n!}{n}=(n-1)!$.
