91Ó°ÊÓ

Use the formula for \(_{n} C_{r}\) to evaluate each expression. $$ _{12} C_{3} $$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1, and common ratio, r. Find \(a_{30}\) when \(a_{1}=8000, r=-\frac{1}{2}.\)

Write a formula for the general term (the nth term of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7},\) the seventh term of the sequence. $$ 3,12,48,192, \dots $$

In Exercises \(15-22,\) find the indicated term of the arithmetic sequence with first term, \(a_{1},\) and common difference, \(d\) Find \(a_{200}\) when \(a_{1}=-40, d=5\)

In Exercises \(23-34,\) write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. $$6,1,-4,-9, \dots$$

A state lottery is designed so that a player chooses six numbers from 1 to 30 on one lottery ticket. What is the probability that a player with one lottery ticket will win? What is the probability of winning if 100 different lottery tickets are purchased?

Use the Fundamental Counting Principle to solve A restaurant offers the following lunch menu. $$ \begin{array}{llll} \text { Main Course } & \text { Vegetables } & \text { Beverages } & \text { Desserts } \\ \text { Ham } & \text { Potatoes } & \text { Coffee } & \text { Cake } \\ \text { Chicken } & \text { Peas } & \text { Tea } & \text { Pie } \\ \text { Fish } & \text { Green beans } & \text { Milk } & \text { Ice cream } \\\ \text { Beef } & & \text { Soda } & \end{array} $$ If one item is selected from each of the four groups, in how many ways can a meal be ordered? Describe two such orders.

Find the sum of the first 20 terms of the arithmetic sequence: \(4,10,16,22, \dots\)

Use the Fundamental Counting Principle to solve Five singers are to perform at a night club. One of the singers insists on being the last performer of the evening. If this singer's request is granted, how many different ways are there to schedule the appearances?

You are dealt one card from a 52 -card deck. Find the probability that you are dealt a red 7 or a black 8 .