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Class 11 Mathematics Chapter 7 Permutations And Combinations Quiz 2 (60 MCQs)

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1. A four-unit passcode is created by choosing two digits and then two letters. How many unique passcodes exist if no number or letter can be repeated?
2. Sarah and Joe are planning trips to three countries this year. There are 7 countries they would like to visit. One trip will be one week long, another two days, and the last one two weeks. How many possibilities are there for their vacation?
3. Evaluate. $\\\_{15}P_3$
4. How many ways can 6 bicycles be parked in a row?
5. For the word MAGIC how many different types of arrangement are possible so that the vowels are always together?
6. How many ways can you listen to 3 songs from a CD that has 12 selections?
7. Eva flips a coin. If she gets heads, she wins $ 4. If she gets tails, she loses $ 3. What is her expected value of a coin flip?
8. Permutation, combination, or neither?The student body of ten students wants to elect apresident, vice president, secretary, and treasurer.
9. A DJ has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?Is this a Permutation or Combination?
10. What is the value of $5!$
11. How would you solve?The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?
12. Find the number of distinct four-letter combinations that can be formed from the letters of the word MATH?
13. An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream. A customer gets to choose a cone and a type of ice cream. How many different 1-scoop ice cream cones can a customer order?
14. A team of 3 members isto be selected from 8 students. In how many ways can the team be chosen if there is no restriction.
15. A team of 3 people is to be selected from 7 women and 6 men. Find the number of different teams that could be selected if there must be more women than men on the team.
16. James purchased 3 shirts, 3 jackets and 2 pairs of pants. How many different outfits using a shirt, a jacket, and pants are possible?
17. Define permutation and combination.
18. Calculate the number of combinations of 6 items taken 2 at a time.
19. If there are 4 different books on mathematics, 3 different books on physics, and 2 different books on chemistry, in how many ways can the books be arranged on a shelf if the books on the same subject must be kept together?
20. What is the multiplication rule in counting principles?
21. In how many ways can the letters of the word "MATH" be arranged?
22. How would you solve?A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?
23. Try something new:Samuel has 5 different colors of pens and 2 different colors of paper. Which model could be used to simulate randomly selecting a pen and a piece of paper?
24. What is the probability of drawing a heart or a club from a standard deck of cards?
25. A team of 17 softball players needs to choose three players to refill the water cooler. How many ways can the selection be made?
26. A committee of 4 members is to be formed from a group of 10 people. How many different committees can be formed?
27. Which of the following is an example of combination?
28. In permutations and combinations, what does the n represent in nPr and nCr?
29. Selecting which nine players will start the game on a 15 person team.
30. Linda is packing to go away for the weekend. She needs to pick 3 of her 10 shirts. How many ways can Linda choose the shirts?
31. A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there?
32. What is C(9, 4)?
33. Which of the following can have no repeating choices and the order affects the amount of possible outcomes?
34. 5 out of 13 students will ride in a car instead of a van. Is this a permutation or a combination?
35. A committee of 8 people is to be chosen from 7 men and 5 women. Find the number of different committees that could be selected if the oldest man or the oldest woman, but not both, must be included in the committee.
36. Permutation or Combination:The student body of 30 students wants to elect a president, vice president, secretary, and treasurer.
37. A combination lock has 7 digits. How many distinct combinations does this lock have if the numbers used have to be 0 through 5?
38. How would you solve?From the 20 DVD's you purchased this past year, you plan to take five with you on vacation. How many different sets of five DVD's can you take?
39. In how many different ways can the letters of the word MAGIC can be formed?
40. Calculate the number of permutations of 5 objects taken 3 at a time.
41. An arrangement of objects in a straight line where the arrangement of the objects is important. It is special case of the counting principle-it tells us the distinct number of arrangements of objects, one after the other, form a set of objects.
42. If P(56, r+6):P(54, r+3) = 30800:1
43. Would you use permutations or combinations to find the number of possible arrangments of 10 students in a line?
44. How many arrangements can be formed from the word MEDIAN?
45. Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?
46. How many different four-person relay teams can be chosen from eight students?
47. In how many different ways can five friends sit for a photograph of five chairs in a row?
48. Jeremiah needs to pick 3 pairs of socks for his trip to Costa Rica. How many ways can he choose if he has 9 pairs?
49. Find how many different 4-digit numbers that are odd and greater than 6000 can be formed using the digits 1, 2, 3, 4, 5, and 6 if no digit is repeated.
50. From a deck of 52 cards, how many ways can you choose 5 cards?
51. In how many ways can 5 red and 4 white balls be drawn from a bag containing 10 red and 8 white balls?
52. Apply the formula for combinations:C(n, r) = n! / (r! * (n-r)!). What is C(8, 3)?
53. If the order of selection does not matter, which method do you use:permutation or combination?
54. How many distinct arrangements are there of the word NEEDLEES?
55. Rob is one of seven children in his family. How many ways can his parents choose four siblings to do chores?
56. Max's cell phone uses a three-digit pin to unlock it. How many different possible ways can he make a pin number using the digits 0-9? No digits repeat.
57. How many ways can the word BASEBALL be arranged?
58. A team of 8 basketball players needs to choose a captain and co-captain.
59. Find the number of possibilities:A group of 25 people are going to run a race. The top 8 finishers advance to finals.
60. If five digits 1, 2, 3, 4, 5 are being given and a three digit code has to be made, then how many such codes can be formed (if repetition of digits is allowed).
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