Five-Minute Check (over Lesson 13–1)

CCSS

Then/Now

New Vocabulary

Key Concept: Factorial

Example 1:Probability and Permutations of n Objects

Key Concept: Permutations

Example 2:Probability and nPr

Key Concept: Permutations with Repetition

Example 3:Probability and Permutations with Repetition

Key Concept: Circular Permutations

Example 4:Probability and Circular Permutations

Key Concept: Combinations

Example 5:Probability and nCr

Over Lesson 13–1

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. 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. 9

B. 15

C. 20

D. 40

Find the number of possible outcomes for the situation. When choosing a cell phone, Terrence has 4 color choices and 5 additional options.

Over Lesson 13–1

A. 40

B. 120

C. 150

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. 144

B. 130

C. 94

D. 72

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?

Content Standards

S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

Mathematical Practices

1 Make sense of problems and persevere in solving them.

4 Model with mathematics.

You used the Fundamental Counting Principle.

• Use permutations with probability.

• Use combinations with probability.

• permutation

• factorial

• circular permutation

• combination

Probability and Permutations of n Objects

TALENT SHOW Eli and Mia, along with 30 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:

Hila, Anisa, and Brant are in a lottery drawing for housing with 40 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?

A.

B.

C.

D.

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

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:

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?

A.

B.

C.

D.

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. B.

C. 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 patter 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?

Probability and Circular Permutations

A. SEATING If 8 students sit at random in the circle of chairs shown, what is the probability that the students sit in the arrangement shown? Explain your reasoning.

Since there is no fixed reference point, this is a circular permutation. So there are (8 – 1)! or 7! distinguishable permutations of the way the students can sit.

Probability and Circular Permutations

Answer: The probability of the students sitting in the

arrangement shown is

Probability and Circular Permutations

B. CRAYONS You purchase a box of 8 crayons. If the crayons are packaged in random order, what is the probability that the crayon on the far left is red? Explain your reasoning.

Since the crayons are packaged in a row, instead of a circle with no fixed reference point, this is a linear permutation. In that case, since there are 8 positions and 1 red crayon, the probability that the crayon on the

far left is red is

Answer:

A. B.

C. D.

A. TABLE SETTINGS If for a birthday party there are 5 people having cake, and there are 5 different colored plates, what is the probability that if chosen at random the plates will be displayed as seen in the order at the right?

A. B.

C. D.

B. CONSTRUCTION A home builder is constructing 6 different models of homes on a major cross street, 5 of which are 2-floored homes, and only 1 home that is 1 floor. If built at random, what is the possibility the 1-floored home will be on the 1st plot of land?

Probability and nCr

A set of alphabet magnets are placed in a bag. If 5 magnets are drawn from the bag at random, what is the probability that they will be the letters a, e, i, o, and u?

Step 1 Since the order in which the magnets are chosen does not matter, the number of possible outcomes in the sample space is the number of combinations of 26 letters taken 5 at a time, 26C5.

Probability and nCr

Step 2 There is only one favorable outcome that all 5 letters are a, e, i, o, and u. The order in which they are chosen is not important.

Step 3 So, the probability of just getting a, e, i, o,

and u is

Answer:

A set of alphabet magnets are placed in a bag. If 4 magnets are drawn from the bag at random, what is the probability that they will be the letters m, a, t, and h?

A. ans

B. ans

C. ans

D. ans