730 CHAPTER 11 Probability In how many ways can they be arranged from left to right if a) they can be arranged in any order? 720 b) the bird must be on the far left? 120 c) the bird must be on the far left and the giraffe must be next to the bird? 24 d) a four-legged animal must be on the far right? 600 33. Team Photo The eight members of the Model United Nations team from Pima Community College are lining up for a photo. a) How many different ways can the eight team members line up? 40,320 b) What is the probability that the members randomly line up in alphabetical order? 1 40,320 34. Family Portrait The seven members of the Snipes family are lining up for a family portrait. a) How many different ways can the seven family members line up? 5040 b) What is the probability that the family members randomly line up in order from youngest to oldest? 1 5040 35. Car Collection Kalin’s sports car collection consists of six different cars manufactured by Bentley, Bugatti, Ferrari, Lamborghini, McLaren, and Mercedes, respectively. Kalin wishes to line up the cars on her driveway to show her friends. a) How many different ways can Kalin line up the cars on her driveway? 720 b) What is the probability that Kalin randomly lines up the cars with the Lamborghini in the first position and the Mercedes in the last position? 1 30 36. Colors of the Spectrum Kayode is building an art display on the campus of Metropolitan Community College. The display will feature arrangements of flags in the colors of the spectrum as shown below. 37. License Plates A license plate is to consist of three digits followed by two uppercase letters. Determine the number of different license plates possible if a) repetition of numbers and letters is permitted. 676,000 b) repetition of numbers and letters is not permitted. 468,000 c) the first and second digits must be odd, and repetition of numbers and letters is not permitted. 104,000 d) the first digit cannot be zero, and repetition of numbers and letters is not permitted. 421,200 38. Possible Phone Numbers A telephone number consists of seven digits with the restriction that the first digit cannot be 0 or 1. Repetition of digits is permitted. a) How many distinct telephone numbers are possible? b) How many distinct telephone numbers are possible with three-digit area codes preceding the seven-digit number, where the first digit of the area code is not 0 or 1? c) Various phone companies are developing phone numbers that use 8 digits instead of 7. How many distinct phone numbers can be made using a three digit area code followed by an eight digit phone number, where the first digit of the area code and the phone number cannot be 0 or 1? 64,000,000,000 39. DJ A disc jockey (DJ) has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song is to be played only once. In how many ways can the DJ play the 9 songs if 8,000,000 6,400,000,000 Red Orange Yellow Green Blue Violet Indigo a) How many different arrangements of the flags are possible? 5040 b) If one of these arrangements is randomly selected, what is the probability that the green flag is in the first position and the blue flag is in the second position? 1 42 a) the songs can be played in any order? 362,880 b) the first song must be a slow song and the last song must be a slow song? 100,800 c) the first two songs must be fast songs? 60,480 40. Meal Delivery Service Fajar has six different meals from a meal delivery service. Three meals include chicken, two meals include beef, and one meal is vegetarian. Fajar will eat one of these meals per day for the next six days. How many different arrangements of meals are possible if a) the meals can be eaten in any order? 720 b) the first meal must include chicken and the last meal must include beef? 144 c) the first two meals must include beef and the last meal must be vegetarian? 12 Dervish45/Shutterstock
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