A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a selection?

A mathematics exam consists of $10$ multiple-choice questions and $5$ open-ended problems in which all work must be shown. If an examinee must answer $8$ of the multiple-choice questions and $3$ of the open-ended problems, in how many ways can the questions and problems be chosen?

Use the formula for

$$_nC_r$$

to solve. How many different committees can be formed from 5 professors and 15 students if each committee is made up of 2 professors and 10 students?

The U.S . Senate consists of 100 members. Senate committees are to be formed so that each of the committees contains the same number of senators and each senator is a member of exactly one committee. The committees are to have more than 2 members but fewer than 50 members. There are various ways that these committee can be formed.

Use the formula for

$$_nC_r$$

to solve. To win in the New York State lottery , one must correctly select 6 numbers from 59 numbers. The order in which the selection is made does not matter. How many different selections are possible?

How many 4-person committees are possible from a group of 9 people if (A) There are no restrictions? (B) Both Jim and Mary must be on the committee? (C) Either Jim or Mary (but not both) must be on the committee?

Use the formula for

$$_nC_r$$

, to solve. Of the 100 people in the U.S. Senate , 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in the selection)?

Use the formula for

$$_nC_r$$

, to solve. There are 14 standbys who hope to get seats on a flight, but only 6 seats are available on the plane. How many different ways can the 6 people be selected?

Use the formula for

$$_nC_r$$

to solve. A four-person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?

Use a graphing calculator to graph the rational function

$$f ( x ) = \frac { 3 x + 2 } { x }$$

. From the graph, determine the equations of the horizontal and vertical asymptotes and the domain and range.

How would the removal of a person's lymph nodes affect the body's ability to fight disease?

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. -If f(x) = sin²(2x), then f’(x) = 2(sin 2x)(cos 2x).

Fifty people purchase raffle tickets. Three winning tickets are selected at random. If each prize is $500, in how many different ways can the prizes be awarded?

In the New York state lottery game "Lotto," a player wins the grand prize by choosing the same group of 6 numbers from 1 through 59 as is chosen by the computer. What is the probability that a player will win the grand prize by playing 5 different tickets?