Over Lesson 13–1 A.A B.B C.C D.D 5-Minute Check 1 A.R 1, 11 B.R 1, R 2 C.R 2, 1 D.R 2, 11 Which is not part of the sample space for the following situation?

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Over Lesson 13–1 A.A B.B C.C D.D 5-Minute Check 1 A.R 1, 11 B.R 1, R 2 C.R 2, 1 D.R 2, 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 5-Minute Check 2 A.W 1, E B.W 2, E C.E, F D.W 1, 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 5-Minute Check 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 5-Minute Check 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?

Then/Now Use permutations with probability. Use factorials

Concept

Example 1 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 1Find 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 2Find 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!.

Example 1 Probability and Permutations of n Objects Step 3Calculate the probability. number of favorable outcomes number of possible outcomes Expand 30! and divide out common factors. Simplify. 1 1 Answer:

A.A B.B C.C D.D Example 1 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?

Concept But then, again, sometimes formulas are not all that great. You may just want to take the first r elements of n! 5 P 2 = P 4 = PERMUTATION (pur-myoo-tay’-shun), an ordered arrangement of objects

Example 2 Probability and n P r 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 1Since 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 ,880

Example 2 Probability and n P r Step 2The 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 3So the probability of the four brown puppies being sold first is Answer: 11,880

A.A B.B C.C D.D Example 2 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?

Example 3 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?

Concept

Example 3 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 1There 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 a calculator.

Example 3 Probability and Permutations with Repetition Step 2There is only one favorable arrangement— bl, gd, bl, gr, bl, gd, bl, gr, bl. Step 3The probability that a permutation of these tiles selected will be in the chosen sequence is Answer:

A.A B.B C.C D.D Example 3 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?