Exam 5: Possibilities and Probabilities

Which of the following is not true of the symbol $\left(\begin{array}{c}11 \\ 3\end{array}\right)$ ?

A shipment of 12 television sets contains one that is damaged. In how many ways can an inspector choose 3 of the televisions to inspect so that: -the defective item is not included?

In the past eight Friday nights, a student has gone to the same rock music club on five occasions. The claim that the probability is $\frac{5}{8}$ that the student will attend the same club next Friday is based on

The number of five-player basketball teams that can be formed from a group of 11 players is _______.

Two families, each consisting of a husband, a wife, two sons, and one daughter, are planning to see a movie together and sit together in the same row. In how many ways can they be seated if: -all the males are to sit together and all of the females are to sit together?

After two vice presidents are selected from 9 division managers, 3 other promotions will be granted. From the remaining division managers, how many ways can the new promotions be granted?

A balanced die is rolled. Find the probability of getting: -an odd number.

Two vice presidents are to be selected from the division managers in a certain company. If there are 9 division managers, in how many ways can the vice presidents be selected?

A magazine reader wants to subscribe to three magazines from a choice of eight magazines. The number of ways this can be done is $\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{3 \cdot 2 \cdot 1}$

A shipment of 12 television sets contains one that is damaged. In how many ways can an inspector choose 3 of the televisions to inspect so that: -the defective item is included?

A restaurant menu has eight main courses, five appetizers, six desserts, and four beverages. The number of ways that a patron can select a meal with one appetizer, one main course, one dessert, and one beverage is _______.

The expression 7 ! 3 ! is equal to 10 !.

If 3 of 16 tax returns contain errors, and 7 of them are randomly chosen for audit, what is the probability that: -exactly two of the returns with errors are audited?

If 3 of 16 tax returns contain errors, and 7 of them are randomly chosen for audit, what is the probability that: -none of the returns with errors is audited?

A group of investors wants to hire a team of 4 accountants and 2 financial planners. If the investors are considering 8 accountants and 5 financial planners:} -how many six-person teams can be hired if no attention is paid to profession?

A cable TV company has 10 channel offerings. One option is that a subscriber may select any four channels. In how many ways can a subscriber make his/her selection?

The probability of selecting a defective component from 20 components, 3 of which are defective, is $\frac{3}{20}$ . This is an example of

Two restaurants are to be built at locations selected from a choice of 11 locations. The number of ways selecting the locations for the two restaurants is

The value ${ }_{7} P_{3}$ is _______.

I have 11 shirts, but only four hangers. In how many ways can I choose four of the shirts to hang in which the arrangement of the shirts in my closet makes a difference to me?