1. In how many ways can an MVP be selected in a league with 9 teams and each team has 12 players in its roster? 108 2. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? 756 3. How many different ways can 7 people – A B C D E F and G – sit in a row at a movie theatre if A and B must sit together? 1440 4. How many ways can 6 different video game cartridges be arranged on a shelf? 720 5. In how many ways can 6 people seat around a table? 120 6. In how many ways can you select a president a secretary and a treasurer for a class of 30 students? 24360 7. If an experiment consists of throwing a die and then drawing a letter at random from the English Alphabet, how many points are in the sample space? 156 8. A company has 2,844 employees. Each of the employee is to be given an ID number consist of one letter followed by two digits. Is it possible to give each employee a distinct ID number: Yes or No? No 9. In how many ways can 6 people seat in a row? 720 10.A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular? 8.718E10 11.A witness to a hit and run accident told the police that the license number contained the letters RLH followed by 3 digits, the first of which is a 5. If the witness cannot recall the last 2 digits, but is certain that all 3 digits are different, find the maximum number of automobile registrations that the police may have to check. 72 12.In how many ways can 10 students be arranged in a row of a class picture if Joseph and Jamie want to stand to each other and Marc and Leonna also insist on sitting next to each other? 161280 13.Concerning a car license plate in the Philippines (3 letters, 3 numbers). How many plates can be formed if the 2nd letter is vowel while the other letters are consonant? 2205000 14.In how many ways can six different rings be worn on for fingers of one hand? 15 15.In how many ways can Emilie hang 8 pictures in a horizontal row? 40320 16.How many different number can be formed using all the digits of the number 882,255? 90 17.A committee including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committee can be formed from the group? 59400 18.There are 12 distinct books composed of five Mathematics and four English and three Science books to be arranged in a shelf. In how many ways can these books be put in a shelf if a random order is needed? 479001600 19.If a car dealer has 5 model line-up and each model has 6 colors to choose from, how many ways can customer choose his car? 30
20.The ice cream shop offers 31 flavors. You order a double-scoop cone. In how many different ways can the clerk put the ice cream on the cone two different flavors? 930 21.How many 3 digit numbers can we make using the digits 2, 3, 4, 5, and 6 without repetitions? 60 22.In a qualifying race for an Olympic road cycling event, 15 men competed for 5 slots. How many different ways could the top 5 slots be arranged which the men finished mattered? 360360 23.How many different 4-letter permutations can be formed from the letters in the word “DECAGON”? 840 24.How many 5-digit zip codes are possible if digits can be repeated? 100000 25.How many permutation are there of the word COMMITTEE? 45360 26.How many 4 digit numbers can we make using the digits 3, 6, 7 and 8 without repetitions? 24 27.On a trip to Pagudpud, Jeff went to visit 4 of the 10 horizontal sites. If the order of the visit matters, in how many ways can he plan the trip? 5040 28.If there are 24 contestants in a pageant, in how many different ways can they place 1st, 2nd, and 3rd? 12144 29.A physics test consists of 25 true/false questions. How many different possible answer keys can be made? 33554432 30.Anne owns 6 pair of jeans, 12 clean t-shirts and 4 pairs of shoes. How many outfits can she create? 288 31.How many 5-digit zip codes are possible if there cannot be repetitions? 30240 32.In how many ways can a caravan of 8 covered wagons from Arizona be arranged in a circle? 5040 33.How many 6 letter words can we make using the letters in the word LIBERTY without repetitions? 5040 34.There are 2 major roads from city X to city Y and 4 major roads from city Y to city Z. How many different trips can be made from city X to … 8 35.A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters? 792 36.How many different numbers can be formed using all the digits of the number 887,711? 90 37.In how many ways can 6 people seat if there are only 3 seats available? 120 38.Concerning a car license plate in the Philippines (3 letters, 3 numbers). How many plates can be formed if not condition is imposed? 17576000 39.Concerning a car license plate in the Philippines (3 letters and 3 numbers). How many plates can be formed if the first and last letter are different? 16900000 40.How many even five digit whole numbers are there? 45000 41.If there are seven doors providing to a building, in how many ways can a person enter the building by one door and leave by a different door? 42 42.There are 10 men attending a directors meeting, how many handshakes were exchanged between the men? 45 43.In how many ways can 6 people seat if 3 people insisted to be seated together? 144 44.In how many ways can 6 people seat if a pair don’t want to be together? 480
45.Telephone numbers consists of seven digits, the first digit cannot be 0 or 1. How many telephone numbers are possible? 8000000 46.In how many ways can 4 couples be seated in a row if each of the couple seats beside each other? 384 47.For her literature course, Rachel has to choose one novel to study from a list of four, one poem from a list of six and one short story from a list of five. How many different choices does Rachel have? 120 48.There are 20 people who work in an office. Four of these people are selected to go to the same conference together. How many selections are possible? 4845 49.There are 12 distinct books composed of five Mathematics and four English and three Science books to be arranged in a shelf. In how many ways can these books be put in a shelf if the same subjects must be put together? 103680 50.Derek must choose a four-digit PIN. Each digit can be choose from 0 to 9. How many possible PIN can Derek choose? 10000 51.A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden lies beside a horizontal pathway? 1.308E12 52.Find the number of ways to assign 12 students to 3 committees, A, B, C, with members 4, 3 and 5, respectively. 27720 53.A lock contains 5 digits in its code. How many codes can be formed if there are no restrictions? 100000 54.A movie theatre sells 3 sizes of popcorn (small, medium, and large) with3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased? 9 55.There are 12 distinct books composed of five Mathematics and four English and three Science books to be arranged in a shelf. In how many ways can these books be put in a shelf if the English and Science books must be together? 3628800 56.How many odd numbers are there greater than 1,000 but less than 100,000? 49500 57.How many ways can a baseball manager arrange a batting order of 9 players? 362880
58.A lock contains 5 digits in its code. How many codes can be formed if the digits cannot all be the same? 59.In how many ways can you select 4 delegates to attend a seminar from 4 supervisors, 3 managers, and 3 assistant managers if 2 of the delegates are supervisor? 60.A lock contains 5 digits in its code. How many codes can be formed if the odd-placed digits are odd while the even-placed ones… 61.There are 12 distinct books composed of five Mathematics and four English and three Science books to be arranged in a shelf. In how many ways … if only the English books must be together? 62.A buyer decides to stock 8 different posters. How many ways can she select and arrange these 8 posters if there are 20 from which to choose? 5079110400 63.in the Philippines it is proposed that license plates will consist of 2 letter followed by 4 numbers, if there are 26 letters and 10 digits how many possible license plates can be issued? 6760000 64.In a regional spelling bee, the 8 finalist consist of 3 boys and 5 girls. Find the number of sample points in the sample space S, for the number of possible orders at the conclusion of the contest for the first 3 positions. 336 65.Concerning a car license plate in the Philippines (3 letters, 3 numbers). How many plates can be formed if the first letter comes from the word statistics, second letter is different from the first, the last letter is consonant, and the digits are all lower than 5? 328125 66.A lock contains 5 digits in its code. How many codes can be form if all digits must be different? 30240