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Class 11 Mathematics Chapter 7 Permutations And Combinations Quiz 8 (50 MCQs)

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1. Grant has five pairs of pants, nine shirts, and six ties. How many different outfits can he make consisting of one pair of pants, one shirt, and one tie?
2. Rob and Mary are planning trips to nine countries this year. They are deciding which countries to skip. Is this a permutation or a combination?
3. Evaluate $\frac{8!}{4!}$
4. What is the probability of choosing 2 female senators if there are 19 female senators and 81 male senators?
5. When order is not important, we use $n_{C_r}$
6. A committee of four is to be selected from 7 men and 5 women. A brother and sister, Ken and Betty, are among the 7 men and 5 women. Find how many different committees of four could be selected so that there are two male and two female members which must include either Ken or Betty but not both.
7. When does the order in which you are choose not matter?
8. In how many ways can the letters of the word BALLOON be arranged such that the two L's are together?
9. Let us suppose we have 12 adults and 10 kids as an audience of a certain show. Find the number of ways the host can select three persons from the audiences to volunteer. The choice must contain two kids and one adult.
10. How many distinct words can be formed using the word MINIMUM?
11. Find how many 4-digit odd numbers and less than 3000 that can be obtained from the digits:1, 2, 3, 4, 5, 6, and 7.
12. Find the total number of outcomes for picking a day of the week and a month of the year.
13. How many different selections of 6 books can be made from 11 different books, if two particular books are always selected?
14. How many ways can 5 persons seat if there are 10 vacant seats in a van?
15. You are setting the combination on a three-digit lock. You want to use the numbers 123 but don't care what order they are in. How many possible combinations are there?
16. . There are 4 black, 5 red and 6 green balls. We have to select 3 balls. In how many different ways we can select atleast one red ball.
17. How many different groups of 6 children can be chosen from a class of 18 children if the class contains one set of twins who must not be separated?
18. Permutation or Combination:Willie and Paul are planning trips to two countries this year. There are 10 countries they would like to visit. One trip will be one week long and the other two weeks.
19. What is the number of arrangements of the letters in the word 'MARCH' where the repetition of letters is not allowed?
20. How many different 10-letter arrangements can be made from the word BASKETBALL?
21. In a poetry-telling competition 4 boys and 6 girls performed excellenty. For a school celebration 3 boys and 3 girls need to be chosen from them. In how many ways can we do so?
22. In how many ways can the word ARRANGE be rearranged if there is no restriction.
23. In permutations and combinations, what does the r represent in nPr and nCr?
24. What is 8C4 (combinations of 8 taken 4 at a time)?
25. Heather must choose a PIN code for her ATM card. The pin is a 4 digit code. How many possible PIN numbers are there?
26. Picking 5 cards from a deck of cards.
27. Tracy wants to display 3 of 5 pictures on her wall in a straight line. How many ways can she arrange the pictures?
28. Find out the number of distinctive words that can be formed using the word GOOD.
29. A ..... is an arrangement of objects in which the order IS important
30. Which is the correct set up for $_{32}C_7$
31. How many identification code are possible by using 3 letters if no letter may be repeated?
32. What is the probability of selecting 3 red balls from a bag containing 5 red balls and 7 blue balls without replacement?
33. A team of 15 basketball players need to choose a Captain & a Co-captain. How many ways can that selection be made?
34. Thirty people report for jury duty. How many different 12-person juries can be chosen?
35. Permutation, combination, or neither?You have 4 framed portraits. How many ways can you arrange all 4 of them on the top of your bookshelf?
36. A 5-character password is to be chosen from the letters A, B, C, D, E, and the digits 4, 5, 6, 7. Each letter or digit may be used only once. Find the number of different passwords that can be chosen if the password contains 2 letters followed by 3 digits.
37. Permutation, combination, or neither?You are setting a combination on a three-digit lock usingthe numbers 0-9.
38. How many different ways can a president, vice-president, and secretary be chosen from a club of 10 members?
39. Identify the situation:Choosing first-, second-, and third-place winners of an art competition.
40. Picking two paint colors for your room.
41. Permutation, combination, or neither?A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
42. Calculate the number of combinations of 6 objects taken 2 at a time.
43. When three-digit telephone area codes were first put in place, the first number could be any digit (2-9), the second number could only be 0 or 1, and the third could be any digit (0-9). How many possible area codes can be created with this format?
44. How many 4-card hands that contain 3 hearts and 1 spade can be chosen from a 52-card deck?
45. We roll a die five times and write down the numbers we get in the order we get them, thus we obtain a 5-digit number. How many different numbers can be obtained in this way?
46. Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is
47. 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?
48. Runners finishing top three in a race to qualify for the Olympics. The order they finish in is irrelevant as long as they are top three.
49. How many ways can you arrange 7 books on a shelf?
50. How many ways can you choose 3 fruits from a basket of 10?
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