Over Lesson 13–1

A. A

B. B

C. C

D. D

A. R1, 11

B. R1, R2

C. R2, 1

D. R2, 11

Which is not part of the sample space for the following situation? George can eat at two different restaurants on his college campus. He has an hour break at 11:00 and at 1:00.

Over Lesson 13–1

A. A

B. B

C. C

D. D

A. W1, E

B. W2, E

C. E, F

D. W1, F

Which is not part of the sample space for the following situation? An editor has two writers available to write a story. They can either write a factual piece or an editorial.

Over Lesson 13–1

A. A

B. B

C. C

D. D

160

Find the number of possible outcomes for the situation. In a cafeteria there are 4 choices for a main dish, 4 choices for a side dish, 5 choices of drinks, and 2 choices for dessert.

Over Lesson 13–1

A. A

B. B

C. C

D. D

144

For her birthday, Trina received a new wardrobe consisting of 6 shirts, 4 pairs of pants, 2 skirts,and 3 pairs of shoes. How many new outfits can she make?

• Use permutations with probability.

• Use factorials

Probability and Permutations of n Objects

TALENT SHOW Eli and Mia, along with 28 other people, sign up to audition for a talent show. Contestants are called at random to perform for the judges. What is the probability that Eli will be called to perform first and Mia will be called second?

Step 1 Find the number of possible outcomes in the sample space. This is the number of permutations of the order of the 30 contestants, or 30!.

Step 2 Find the number of favorable outcomes. This is the number of permutations of the other contestants given that Eli is first and Mia is second, which is (30 – 2)! or 28!.

Probability and Permutations of n Objects

Step 3 Calculate the probability.

number of favorable outcomesnumber of possible outcomes

Expand 30! and divide out common factors.

Simplify.

1

1

Answer:

• We can also think about this logically:– for the first selection, how many people are

there to choose from? • 30 people, only on of which is Eli, so the probability

is

– for the second selection, how many people are left to choose from?• 29 people, only on of which is Mia, so the

probability is

• =

A. A

B. B

C. C

D. D

Hila, Anisa, and Brant are in a lottery drawing for housing with 37 other students to choose their dorm rooms. If the students are chosen in random order, what is the probability that Hila is chosen first, Anisa second, and Brant third?

• But then, again, sometimes formulas are not all that great.

• You may just want to take the first r elements of n!

• 5P2 = 5 • 4• 6P4 = 6 • 5 • 4 • 3

PERMUTATION (pur-myoo-tay’-shun), an ordered arrangement of objects

Probability and nPr

There are 12 puppies for sale at the local pet shop. Four are brown, four are black, three are spotted, and one is white. What is the probability that all the brown puppies will be sold first?

Step 1 Since the order that the puppies are sold is important, this problem relates to permutation. The number of possible outcomes in the sample space is the number of permutations of 12 puppies taken 4 at a time.

1

1

P4 = 12 • 11 • 10 • 9 = 11,880

using the formula:11,880

Probability and nPr

Step 2 The number of favorable outcomes is the number of permutations of the 4 brown puppies in their specific positions. This is 4! or 24 favorable outcomes.

Step 3 So the probability of the four brown

puppies being sold first is

Answer:

11,880

A. A

B. B

C. C

D. D

There are 24 people in a hula-hoop contest. Five of them are part of the Garcia family. If everyone in the contest is equally as good at hula-hooping, what is the probability that the Garcia family finishes in the top five spots?

Probability and Permutations with Repetition

TILES A box of floor tiles contains 5 blue (bl) tiles, 2 gold (gd) tiles, and 2 green (gr) tiles in random order. The desired pattern is bl, gd, bl, gr, bl, gd, bl, gr, and bl. If you selected a permutation of these tiles at random, what is the probability that they would be chosen in the correct sequence?

Probability and Permutations with Repetition

TILES A box of floor tiles contains 5 blue (bl) tiles, 2 gold (gd) tiles, and 2 green (gr) tiles in random order. The desired pattern is bl, gd, bl, gr, bl, gd, bl, gr, and bl. If you selected a permutation of these tiles at random, what is the probability that they would be chosen in the correct sequence?

Step 1 There is a total of 9 tiles. Of these tiles, blue occurs 5 times, gold occurs 2 times, and green occurs 2 times. So the number of distinguishable permutations of these tiles is

Use acalculator.

Probability and Permutations with Repetition

Step 2 There is only one favorable arrangement—bl, gd, bl, gr, bl, gd, bl, gr, bl.

Step 3 The probability that a permutation of these tiles selected will be in the chosen

sequence is

Answer:

A. A

B. B

C. C

D. D

TILES A box of floor tiles contains 3 red (rd) tiles, 3 purple (pr) tiles, and 2 orange (or) tiles in random order. The desired pattern is rd, rd, pr , pr, or, rd, pr, and or. If you selected a permutation of these tiles at random, what is the probability that they would be chosen in the correct sequence?