pencil, red pen, highlighter, GP notebook, calculator U11D7 Have out: Bellwork: Answer the following 1. Determine the values without using a calculator. a) b) 2. There are 30 Algebra 2 students in a class. 21 are selected to attend a math conference. How many different ways can the students be selected? 3. There are 5 front row seats available in the Kodak Theatre for a taping of “American Idol.” 24 pre-teen girls rush to the front to grab the seats. In how many ways can they be seated in the front row? total:

Bellwork: 1. Determine the values without using a calculator. a) b) 3 +1 +1 +1 +1 3 +1 1 +1

Bellwork: 2. There are 30 Algebra 2 students in a class. 21 are selected to attend a math conference. How many different ways can the students be selected? Does order matter? No We don’t care who is picked first or last. Is there repetition? No Once someone is picked, the person will not be selected again. This is a combination! +1 +1 +1 total:

Bellwork: 3. There are 5 front row seats available in the Kodak Theatre for a taping of “American Idol.” 24 pre-teen girls rush to the front to grab the seats. In how many ways can they be seated in the front row? Does order matter? Yes There are only 5 seats, and we are concerned with how the girls are seated. Who will have the first seat? second seat? etc. Is there repetition? No Once someone is picked, the person will not be selected again. This is a permutation! +1 +1 +1

It’s time to grade the QUIZ!!! Clear your desk except for a red pen.

Card Hands Take out the worksheet Be sure to take out your playing card reference sheet we used during the last chapter. Recall that there are 52 cards in a regular deck of cards. Answer the following. a) Does order matter when playing cards? No, order DOES NOT matter. For example: is the same as

(If there are repeats, then someone is a cheat.) Order DOES NOT matter. is the same as You still have the same cards, but they are not in the same order. It doesn’t matter what order you have the cards. There is also NO REPETITION. For instance, this means that we will not have a card hand with 2 jacks of heart. (If there are repeats, then someone is a cheat.) Better be no cheatin’, ya hear?

b) How many ways are there to choose 3 cards from a set of 52? order does not matter, no repetition, combination c) If you pulled out all 13 spades from a deck, then how many ways are there to choose 3 cards out the spades? d) If you pulled out all 12 face cards from a deck, then how many ways are there to choose 3 cards out the face cards?

e) Using a standard deck of cards, what is the probability of choosing 3 spades from a card deck to make a 3-card hand? Use the answers from parts (b) and (c) to help you solve the problem. # of possible 3–card hands of that are all spades. P (3 spades) = Total # of possible 3–card hands If you were playing cards, then this means that there is a 1.3% chance that you will be dealt all spades in a 3–card hand. BTW, I am showing the decimal answers (and percentages), but you DO NOT need to show these. Fractional answers are good enough!

Do parts (g) and (h) on your own. f) Using a standard deck of cards, what is the probability of dealing 3 face cards from a card deck to make a 3-card hand? Use the answers from parts (b) and (d) to help you solve the problem. # of possible 3–card hands of that are all face cards. P (3 face cards) = Total # of possible 3–card hands This means that there is about 1% chance that you will be dealt all face cards in a 3–card hand. Do parts (g) and (h) on your own.

g) What is the probability of dealing 2 hearts out of all the hearts in the deck for a 2–card hand? # of possible 2–card hands of that are all hearts. P (2 hearts) = Total # of possible 2–card hands This means that there is about 5.9% chance that you will be dealt all hearts in a 2–card hand.

h) What is probability of dealing 4 clubs out of all the clubs in the deck for a 4–card hand? # of possible 4–card hands of that are all clubs. P (4 clubs) = Total # of possible 4–card hands This means that there is about 0.3% chance that you will be dealt all clubs in a 4–card hand.

2. Suppose you draw 5 cards from a regular deck of cards 2. Suppose you draw 5 cards from a regular deck of cards. Answer the following. How many ways are there to choose 5 cards from a set of 52? When we discuss the probabilities for 5–card hands, we will use this answer for the denominator.

b) What is the probability of getting a five card hand that is all black? # of possible 5–card hands of that are all black. P (all black) = Total # of possible 5–card hands c) What is the probability of getting a five card hand that is all spades? # of possible 5–card hands of that are all spades. P (all spades) = Total # of possible 5–card hands

d) What is the probability of getting 4 red cards and 1 black card? # of ways to get 4 cards from all red cards # of ways to get 1 card from all black cards P (4 R, 1 B) = Total # of possible 5–card hands

e) What is the probability of getting 3 clubs and 2 diamonds cards? # of ways to get 3 cards from all clubs # of ways to get 2 cards from all diamonds P (3 ♣, 2 ♦) = Total # of possible 5–card hands

Try parts (g) - (j) on your own. f) What is the probability of getting exactly 3 diamonds and 2 other cards? # of ways to get 3 cards from all diamonds # of ways to get 2 other cards (non–diamonds) P (3 ♦, 2 others) = Total # of possible 5–card hands Try parts (g) - (j) on your own.

g) What is the probability of getting exactly 4 hearts and 1 other card? # of ways to get 4 cards from all hearts # of ways to get 1 other card (non–heart) P (4 ♥, 1 other) = Total # of possible 5–card hands

h) What is the probability of getting 3 spades and 2 red cards? # of ways to get 3 cards from all spades # of ways to get 2 cards from all reds P (3 ♠, 2 Red) = Total # of possible 5–card hands

i) What is the probability of getting 4 black cards and 1 heart? # of ways to get 4 cards from all black # of ways to get 1 card from all hearts P (4 B, 1 ♥) = Total # of possible 5–card hands

j) What is the probability of getting 2 diamonds, 2 hearts, and 1 club? # of ways to get 2 cards from all diamonds # of ways to get 2 cards from all hearts # of ways to get 1 card from all clubs P (2♦, 2♥, 1♣) = Total # of possible 5–card hands

Finish the worksheets.