Exam 5: Possibilities and Probabilities

Give the number of ways a student can mark her answers to a multiple choice test if there are three questions with eight choices each

A new campus project requires a committee of 5 students which will include 2 seniors and 3 juniors. There are 6 available seniors and 8 available juniors. -In how many ways can the required committee be chosen?

The probability of rolling a three in one roll of an ordinary die is $\frac{1}{6}$ . This is an example of the frequency interpretation of probability.

The multiplication of choices principle states that if an experiment is repeated again and again, the proportion of successes will tend to approach the probability that any one outcome will be a success.

A student can play 0, 1, or 2 hours of racquetball on any given night. Construct a tree diagram to determine the number of ways that in three nights he can play for a total of five hours.

The number of seven-digit phone numbers that can be formed that begin with 353 with not all of the last four digits 0 is 94 .

In how many ways can 12 persons be arranged in a circle?

In an 8-horse race, the number of ways that 3 horses can finish first, second, and third (order matters) is given by

A student has time to see four films on his vacation. If he is selecting the movies from a total of nine choices, how many ways can he choose the films?

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 of the children are to sit together and all of the adults are to sit together?

A multiple choice test has 10 questions with 4 choices for each question. The number of ways a student can answer all 10 questions is

The value of $\left(\begin{array}{l}7 \\ 3\end{array}\right)$ is _______.

Two cards are drawn from a well-shuffled deck of 52 playing cards.} -What is the probability of getting two jacks?

The number of ways that 4 students can be selected from 30 students in a class to fill 4 seats (if order matters) is $\frac{30 \cdot 29 \cdot 28 \cdot 27}{4 \cdot 3 \cdot 2 \cdot 1}$

There are six baseball teams in the American League's Eastern division. In how many ways can:} -all six teams finish first through sixth?

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: -each family is to sit together?

Which of the following is false?

A student has seven items of living room furniture and room for five items in his living room. Assuming that any of the seven items can be placed in any of the five locations, in how many ways can the student arrange his living room with the furniture?

The number of three person committees that can be formed from eight people is the same as the number of three-letter words that can be formed from the letters a, b, c, d, e, f, g, h with no repetitions.

If the president is considering the elimination of seven federal programs but is selecting only three of the seven to eliminate, the number of ways he can select the programs is _______.