4) Neo wants to download 6 different songs. He only has enough money to purchase 4. In how many ways can he select 4 or 6 songs to purchase?

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1 Section 4.8: Combinations Homework #1-17 1) An ice cream parlor has 20 different flavors. Cynthia orders a banana split and has to select 3 different flavors. How many different selections are possible? 2) A textbook search committee is considering 8 books for possible adoption. The committee has decided to select three of the eight for further consideration. In how many ways can they do so? 3) The drama club is planning a trip to New York. While in New York they want to attend 3 plays out of 10 plays they would like to see. How many different groups of 3 plays can they select to attend? 4) Neo wants to download 6 different songs. He only has enough money to purchase 4. In how many ways can he select 4 or 6 songs to purchase? 5) In how many ways can you select a committee of 4 students out of 12 students? 6) In how many ways can you select 3 different vegetables from 8 vegetables?

2 7) 3 different varieties of flowers are going to be placed in a vase. There are 5 different flowers to choose from. How many combinations can be made from the 5 varieties of flowers? 8) How many 3 topping pizzas could be made if you have 10 toppings to choose from (assume each topping can only be used once)? 9) The US senate consists of 100 senators, two from each state. A committee consisting of five senators is to be formed. How many are possible? 10) There are 6 restaurants you would like to try on your next vacation. You only have time to try 4 of them when you go on vacation. How many groups of restaurants can you choose? 11) You need to upload a few videos to watch on a plane. You only have storage capacity to add 5 new videos, but have 12 videos to choose from. How many combinations videos can you choose?

3 12) How many groups of 2 sevens can be made from the 4 sevens in a deck of cards? 13) How many groups of 3 kings can be made from the 4 kings in a deck of cards? 14) How many groups of 4 hearts can be made from the 13 hearts in a deck of cards? 15) How many groups of 3 spades can be made from the 13 spades in a deck of cards? 16) How many groups of 2 black cards can be made from the 26 black cards in a deck of cards? 17) How many groups of 5 red cards can be made from the 26 red cards in a deck of cards?

4 Homework # ) On an English test, Tito must write an essay for 3 of 5 questions in part one and 4 of 6 questions in part two. How many different combinations of questions can he answer? 19) A couple is planning a party. They need to pick 2 of 6 dinners to offer, and 3 of 5 desserts. How many different combinations can they pick? 20) An 8 person committee is being formed from a club that has 10 seniors and 8 juniors. How many committees can be formed if the committee must have 6 seniors and 2 juniors? 21) 6 members of a club will be selected to attend a conference. The club has 8 female and 7 male members. How many different groups can be selected if 3 male and 3 females must be selected? 22) A club plans to visit 3 of 5 landmarks in California and 2 of 4 landmarks in Oregon. How many different groups of sites can they select?

5 23) At a medical research center an experimental drug is to be given to 12 people, 6 men and 6 women. If 10 men and 9 women have volunteered to be given the drug, in how many ways can the researcher choose the 12 people to be given the drug? 24) At a medical research center an experimental drug is to be given to 20 people, 12 children and 8 adults. If 15 children and 9 adults have volunteered to be given the drug, in how many ways can the researcher choose the 20 people to be given the drug? 25) Michael is sent to the store to get 5 different bottles of regular soda and 3 different bottles of diet soda. If there are 10 different types of regular soda, and 7 different types of diet soda to choose from, how many different choices does Michael have? 26) A couple is throwing a party. They need to pick 5 different kinds of beer from the 12 beers being offered, and they need to pick 4 snacks from the 9 snacks being offered. How many different choices do they have?

6 27) How many groups of 2 sevens and 3 threes can be made from the 4 sevens and 4 threes in a deck of cards? 28) How many groups of 3 kings and 1 jack can be made from the 4 kings and 4 jacks in a deck of cards? 29) How many groups of 4 hearts and 2 spades can be made from the 13 hearts and 13 spades in a deck of cards? 30) How many groups of 3 spades and 2 clubs can be made from the 13 spades and 13 clubs in a deck of cards? 31) How many groups of 2 black cards and 4 red cards can be made from the 26 black cards and 26 red cards in a deck of cards? 32) How many groups of 5 red cards and 1 black card can be made from the 26 red cards and 26 black cards in a deck of cards?

7 Answers: 1) 20C3 = ) 10C3 = 120 5) 12C4 = 495 7) 5C3= 10 9) 100C5 = 75,287,520 11) 12C5 =792 13) 4C3 = 4 15) 13C3 =286 17) 26C5 =65,780 19) 6C2 * 5C3 = 15*10 = ) 7C3 * 8C3 = 35*56 = ) 10C6 * 9C6 = 210*84 = 17,640 25) 10C5 * 7C3 = 252*35 = 8,820 27) 4C3 * 4C2 = 4*6 = 24 29) 13C4 * 13C2 = 715 * 78 = 55,770 31) 26C2 * 26C4 = 325*14950 = 4,858,750