need it ASAP

1. If the digits {O, 1, 2, 3, 4, 5, 6} are used to construct a 3-digit number, find the number of possibilities under each of the restrictions below. (Note: the number 012., for example, is NOT considered a 3 digit number)

(1) a. No restrictions on digits.

(2) b. Odd 3-digit numbers.

C:?) c. 3-digit numbers without repeated digits.

) d. 3-digit multiples of 5 without repeated digits.

2. Evaluate each of the following factorial expressions.

Cc>)

a. 6! b.

70!

8!

61

12!

c. 65!

d. 8!4!

c;)

e. ·Does the expression represent a permutation or combinatibn? Write the expression in its symbolic form.

( , )f. Does the expression i,1

represent a permutation or cobination? Write the expression in

its symbolic form.

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3. Answer each item below using the ·set indicated.

a. How many pe:i;mutations of 2 elements taken from the set { a, b,c, d} are possible? List them all.

(3)

c )

b. How many combinations of 3 elements taken from the set {a, b, c, d, e,} are possible? List them all.

4. There are 7 players on a team. The coach must select players for each of the categories listed below. Determine the total number of ways the coach can make each decision.

a. Coach needs 3 players to carry equipment to games.

b. Coach needs 3 players to play Front, 2 players to play Middle, and 1 player to play Back.

c. Coach needs 2 groups of 3 players each to practice against each other.

d. Coach needs a group of 5 or more players.

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(z)

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(2)

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5. Determine the_ number of possible settings for a row of five on-off switches under each condi­ tion.

a. 'There are no restrictions. Each switch can be either on or off.

b. The first and fifth switches must be set the same.

c. At least 2 switches must be on.

d. No two adjacent switches can be set the same>

6. 3 distinct letters are chosen from the set { A, B,C,D,E ,F,G}. Determine the number of subsets that can be formed that include each of the following: (Hint: recall the definition of subset as it relates to the order of the elements)

a. The letter B is in the subset.

b. both the .letters A and E are in the subset.

c. Either A or E is in the subset, but not both.

d. There are more consonants than vowels in the subset.'(The only vowels are A and E in the list above, the others are consonants).

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(2)

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PART &: PROBABILITY

7. ( v )Bill, Jim, and Sam are members of a class ,that has 26 total students. 3 people will be chosen, in order, to give their report. Find the probability (correct to six decimals) of each evet described below.

a. Bill, Jim; and Sam are selected, in that exact order.

b. Bill, Jim, and Sam are selected, in any order.

c. At least one of Bill, Jim, or Sam is chosen to give their report.

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8.. Suppose 2 distinct numbers are chosen, one at a time, randomly from the set {1, 2, 3, 4, 5}.

a. Find the probability that the sum of the numbers is 5.

b. Find the probability that the sum of the numbers is even.

c. Find the probability that the sum is even or greater than 5.

d. Find the probability that the first number is 3 and the second number is even.

e. Find the probability that the second number is odd, given that the first number .is a 3.

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9. Suppose an experiment consists ofrolling 3 different colored six-sided dice (Red, Blue, Green). Find the following:

a. the number of total possible outcomes.

b. The probability that the sum of the dice equals 6. (Hint: there are different ways that 3 numbers can add up to be six.)

c. The probability that the numbers showing will all be different.

10. A jar contains 7 colored balls: 4 are Red, 2 are Blue, and 1 is Yellow. Tim and Jon each select one ball from the jar, in that order, without replacement. Find the probability of each of the events below.

a. Both select a Red ball.

(2)

b. Both select the same colored ball.

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c. Jon selects a Red ball, ·given Tim selects a Yellow ball.

d. Jon selects a Red ball.

5 .

11. The table below is from the most recent U.S. census and compiles information related to marital status and gender. The values in the table are percentages of the total number of people surveyed during the census. Use the table to answer the questions that follow.

Marital status

· Suppose a U.S. resident 18 years or older is selected at random. Answer each question below.

a. Find the probability that the person is female and widowed.

b. Suppose the person is inale. \Vhat is the probability he was never married?

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(5')

c. \Vhat proportion of married responents are female?

12. In the picture below, assume each spinner is spun once and the results are added together. Find the probability the sum is greater than 7. Assume for each spinner, there is equally likelihood of landing on each number.

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13. Suppose two cards are dealt successively, without replacement, from a standard 52-card deck.

Find each of the probabilities ,below. ·

(1 )

{2 )

a. A spade second, given a spade is drawn first.

b. Two face cards.

c. Tthe first card is a Jack and the second is a face card.

c J

(1)

d. The second card is a Jack.

14. Tom has a poor attendance record at work. He has a 0.78 probability of being late to work on any given work day. Suppose 3 work days are chosen randomly. (A tree diagram may be helpful)

a. \Vhat is the probability Tom is late to work all three days?

(3)

b. What is the probability Tom is late on exactly two of the days?

c. What is the probability Tom is late at least one of the three days?

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n!

( ( n r) )• nCr = ---

- !r!

n!

· nPr = (n _ r)!

Formulas

· P( A U B) = P( A) + P( B) - P( A nB)

• P( AI B) = n( A n B )

n( B)

· P( AI B) ·P( B) = P( A nB)

· P( BIA) ·P( A) = P( A n B)

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