# Chapter 4 - Probability - 4-6 Counting - Beyond the Basics - Page 183: 38

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 $\frac{n!}{n}=(n-1)!$.

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