91Ó°ÊÓ

In Exercises 9 - 14, determine the sample space for the experiment. Two county supervisors are selected from five supervisors, \( A \), \( B \), \( C \), \( D \), and \( E \), to study a recycling plan.

In Exercises 5 - 14, calculate the binomial coefficient. \( \dbinom{100}{2} \)

In Exercises 5 - 16, determine whether the sequence is geometric. If so, find the common ratio. \( \dfrac{1}{5}, \dfrac{2}{7}, \dfrac{3}{9}, \dfrac{4}{11}, \cdots \)

In Exercises 9-32, write the first five terms of the sequence. (Assume that \( n \) begins with 1.) \( a_n = \left(-\dfrac{1}{2} \right)^n \)

In Exercises 11 - 24, use mathematical induction to prove the formula for every positive integer \( n \). \( 1 + 4 + 7 + 10 + \cdots + \left(3n - 2\right) = \dfrac{n}{2}\left(3n - 1\right) \)

In Exercises 5 - 14, determine whether the sequence is arithmetic. If so, find the common difference. \( 1^2, 2^2, 3^2, 4^2, 5^2, \cdots \)

In Exercises 9 - 14, determine the sample space for the experiment. A sales representative makes presentations about a product in three homes per day. In each home, there may be a sale (denote by \( S \)) or there may be no sale(denote by \( F \)).

In Exercises 15 - 18, evaluate using Pascals Triangle. \( \dbinom{6}{5} \)

In Exercises 5 - 16, determine whether the sequence is geometric. If so, find the common ratio. \( 1, -\sqrt{7}, 7, -7, \sqrt{7}, \cdots \)

In Exercises 15 - 20, find the probability for the experiment of tossing a coin three times. Use the sample space \( S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} \). The probability of getting exactly one tail