Probability Theory Homework

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? This is a combination problem as the order the toppings are picked doesn’t matter. 20C3 = 1140 Answer: 1140 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? Only the 3 plays selected matter and the order they were selected in does not matter. This is a combination problem. 10C3 = 120 Answer: 120 5) In how many ways can you select a committee of 4 students out of 12 students? Committee problems are always combination problems. 12C4 = 495 Answer: 495 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? I need to select 3 of 5 varieties. The order will not matter. 5C3= 10 Answer: 10 9) The US senate consists of 100 senators. A committee consisting of 5 senators is to be formed. How many are possible? This is a committee problem. Every committee problem we solve will be a combination problem. I need to select 5 of the 100 senators. 100C5 = 75,287,520 Answer: 75,287,520 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? The order I select the videos to upload is not important. Only the videos uploaded is important. This is a combination problem 12C5 =792 Answer: 792 13) How many groups of 3 kings can be made from the 4 kings in a deck of cards? Only the cards that are selected make difference. The order is not important and this is a combination problem. 4C3 =4 Answer: 4 15) How many groups of 3 spades can be made from the 13 spades in a deck of cards? Only the cards that are selected make difference. The order is not important and this is a combination problem. 13C3 =286 Answer: 286 17) How many groups of 5 red cards can be made from the 26 red cards in a deck of cards? Only the cards that are selected make difference. The order is not important and this is a combination problem. 26C5 =65,780 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? Choose 2 of 6 dinners Choose 3 of 5 desserts C = 15 6 2 5C3 = 10 15*10 = 150 Answer: 150 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? Choose 3 of 8 men 8C3 = 56 Choose 3 of 7 women 7C3 = 35 56*35 = 1960 Answer: 1960 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? Choose 6 of 10 men 10C6 = 210 210*84 = 17,640 Answer: 17,640 Choose 6 of 9 women 9C6 = 84 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? Choose 5 of 10 regular 10C5 = 252 Choose 3 of 7 diet 7C3 = 35 252*35 Answer: 8,820 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? Choose 2 of 4 sevens 4C2 = 6 Choose 3 of 4 threes 4C3 = 4 6*4 = 24 Answer: 24 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? Choose 4 of 13 hearts 13C4 = 715 Choose 2 of 13 spades 13C2 = 78 715*78 =55,770 Answer: 55,770 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? Choose 2 of 26 black cards 26C2 = 325 325*14950 = 4,858,750 Answer: 4,858,750 Choose 4 of 26 red cards 26C4 = 14,950