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Class 11 Mathematics Chapter 7 Permutations And Combinations Quiz 1 (60 MCQs)

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1. There are 15 applicants for four jobs:Computer Programmer, Software Tester, Manager, and Systems Engineer. Is this a permutation or a combination?
2. You have DVD collection with 20 DVDs. You can only take five DVDs with you on vacation. How many different sets of five DVDs can you take?Is this a Permutation or a Combination?
3. How many ways could you choose 2 different letters from SCHOOL?
4. A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there?
5. The batting order for seven players on a 12 person team. Is this a permutation or a combination?
6. How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?
7. A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there if you cannot reuse a number?
8. In the combination formula 4C2, what does the 'C' represent?
9. Permutation or Combination:Rob and Micaela are planning trips to four countries this year. There are 5 countries they would like to visit. One trip will be one week long, another two days, another two weeks, and the other a month.
10. The company Sea Esta has ten members on its board of directors. In how many different ways can it elect a president, vice-president, secretary and treasurer?
11. Calculate the number of ways to select 2 out of 5 different colored balls.
12. The ski club has 10 members and is choosing three officers for the season. How many ways can they pick a captain, co-captain and secretary?
13. How many ways can you choose 2 books from ashelf of 40 books?
14. A password consists of 4 different letters. How many different passwords can be formed using the letters A, B, C, D, E, and F?
15. What is 5! (5 factorial)?
16. There are 10 men and 6 women working at a company. A hiring committee of 4 staff members is selected by a supervisor.What is the probability that the committee is made up of 3 women and 1 man?
17. Permutation or Combination:A group of 40 people are going to run a race. The top three runners earn gold, silver, and bronze medals.
18. Evaluate $_{10}$P$_{3}$
19. The digits of the number 6378129 are to be arranged so that the resulting 7-digit number is even. Find the number of ways in which this can be done.
20. In how many ways the letters of the word OPPENHEIMER be arranged?
21. Is the order of arrangement important?A hamburger shop offers 8 toppings for customers to make their own burgers. A customer makes his burger by deciding whether or not he wants to add a particular topping. How many types of burgers can the customer make?
22. Billy has 54 marbles. 10 are blue, 9 are green, 25 are red, and 10 are black. What is the probability of drawing out a black marble?
23. Permutation or Combination:You are setting the combination on a four-digit lock. You want to use the numbers 3817 but don't care what order they are in.
24. If three letters are to be chosen from A, B, C, D and E such that repetition is not allowed then in how many ways it can be done?
25. Picking a team of three people out of a group of 10.
26. A dessert is made by choosing from a type of ice cream (chocolate, vanilla, or strawberry), a topping (sprinkles, gummies, nuts, bananas), and a sauce (caramel, hot fudge). How many different sundaes can be made?
27. The batting order for seven players on a 12 person team.
28. At a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
29. If you have 6 different shirts and want to wear 2, how many different combinations can you wear?
30. Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
31. A group of 25 people are going to run a race. The top 8 finishers advance to the finals. How many different groups of 8 are possible?
32. Using the counting principle, how many different two-letter codes can be created using the letters A, B, C, and D without repeating letters?
33. There are 68 juniors at the high school. How many ways can they elect a class president, vice president, and secretary?
34. Find out the distinct four-letter words that can be formed using the word SINGAPORE.
35. There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?
36. How many ways can you arrange the word TOMORROW?
37. On a railway line there are 20 stops. A ticket is needed to travel between any 2 stops. How many different tickets would the government need to prepare to cater to all possibilities?
38. A team of 6 tennis players is to be chosen from 10 tennis players consisting of 7 men and 3 women. Find the number of different teams that could be chosen if the team must include at least 1 woman.
39. A team of 8 basketball players needs to choose a captain and co-captain. Is this a permutation or a combination?
40. A team of 17 softball players needs to choose three players to refill the water cooler. Is this a permutation or a combination?
41. A couple wants to plant some shrubs around a circular walkway. They have seven different shrubs. How many different ways can the shrubs be planted?
42. Rob and Mary are planning trips to nine countries this year. There are 13 countries they would like to visit and are deciding which countries to skip. How many ways can the selection be made?
43. An internet code consists of one digit followed by one letter, The number zero and letter O are excluded. How many codes are possible?
44. Evaluate. $\\_{10}C_4$
45. Find out the number of arrangements that can be made for the word RAINBOW if all the vowels are placed on the even places?
46. How many ways can a teacher choose 5 students out of 13 to ride in a car instead of the van?
47. How many ways can an employer fill four jobs:Computer Programmer, Software Tester, Manager, and Systems Engineer, if they have 15 applicants?
48. There are ten toppings available to make an ice cream sundae. How many ways can Lala choose two?
49. A Permutation is a way in which a set or number of things can be ordered or arranged, where .....
50. A committee of 6 members is to be selected from 5 men and 9 women. Find the number of different committees that could be selected ifthere is at least 1 man on the committee.
51. In how many ways can a committee of 3 people be selected from a group of 10 people?
52. A committee consisting of 7 people is to be selected from 6 teachers, 5 parents and 3 school principals.Calculate the number ways of forming the committee if there are no restrictions.
53. The number of words you can make from the Scrabble tiles M, A, T, H.
54. You put 5 names into a hat, they are:John, Jill, Jack, Justin, and Jeremy. What is the probability of you pulling Jack and Jill?
55. In how many ways can a coach choose three swimmers from among five swimmers?
56. You are dealt 5 cards from a standard deck of playing cards. What is the probability you are dealt a flush? **A flush is all 5 cards of the same suit (order does not matter).
57. If P(22, r+1):P(20, r+2) = 11:52, find r.
58. A team of 5 is to be formed from 8 men and 7 women. How many ways can the team be formed if it must consist of 3 men and 2 women?
59. How many ways can two jellybeans be chosen from a bag of 15 unique jellybeans.
60. In how many ways can the letters of the woed 'HONESTY' be arranged?
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