Bell work An Internet code consists of one digit followed by two letters. The number 0 and the letter “O” are excluded. How many different codes are possible?

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Presentation transcript:

Bell work An Internet code consists of one digit followed by two letters. The number 0 and the letter “O” are excluded. How many different codes are possible? How many different ways can 1st, 2nd, and 3rd place be awarded to 12 contestants at the school spelling bee? How many possible ways can you permute the letters of NEBRASKA?

Section 7-1: Permutations and Combinations Chapter 7 - Probability Section 7-1: Permutations and Combinations

Combinations Definition: A grouping of items in which order does not matter Generally, combinations are lesser quantities than their permutation counterparts total arrangements = nCr = n! (arr. of selected)(arr. of unselected) r! (n-r)!

Examples Michael is going to California on vacation. His vacation package offers eight choices of fun activities to do each day he is there. If he has four days of vacation and three days to do the activities, how many different ways can he choose his adventures?

At a track meet, there are five heats of the one mile race At a track meet, there are five heats of the one mile race. The Creighton team has nine men racing. Three runners will be chosen to race in the first heat. How many ways can three runners be chosen from the team?

Let’s roll five dice. How many ways can we choose two of the resulting dice to roll again? Rachel can choose 1 elective each of the 4 years she is in high school. There are 19 electives to choose from. How many ways can Rene choose her electives?

Now, let’s draw some cards. How many different ways are there to choose a 5-card poker hand from a standard deck of 52? How many ways are there to choose a hand with a two of a kind, and a three of a kind? (Two of the same value, and three of the same value different from the value of the two of a kind)

Guided Practice John is playing Yahtzee and he rolls his five dice. How many ways can he arrange the dice from left to right? How many ways can he choose 3 of the dice to reroll? Betsy is playing poker with her friends. How many different 5-card hands can she be dealt? How many different 5-card hands are possible, if all five cards must be of the same suit? Calculate nCn for any value of n. What does this mean? What does 2C5 mean? Why is this impossible?

Homework Textbook pg. 486-487 #7, 8, 24-29, 33-36

Exit Slip What is the difference between a permutation and a combination? Give an example of when you would use each method. Are the formulas different? How? Which is greater—2C5 or 2P5?