### Permutation and Combination Questions with Answers

**Ques.** The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

(a) 269

(b) 300

(c) 271

(d) 302

**Ques.** The sides *AB,* *BC*, *CA* of a triangle *ABC* have respectively 3, 4 and 5 points lying on them. The number of triangles that can be constructed using these points as vertices is

(a) 205

(b) 220

(c) 210

(d) 240

**Ques.** 12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is

(a) 9 (10 !)

(b) 2(10 !)

(c) 45(8 !)

(d) 10 !

**Ques.** Preeti, Shweta, Reena and Salma have to give lectures to an audience. The organiser can arrange the order of their presentation in

(a) 4 ways

(b) 12 ways

(c)

(d) 24 ways

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**Ques.** Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty

(a) 50

(b) 100

(c) 150

(d) 200

**Ques.** Poonam gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is

(a) 112

(b) 140

(c) 164

(d) 624

**Ques.** A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, then the number of ways in which the car can be filled is

(a) 10

(b) 20

(c) 30

(d) None of these

**Ques.** How many numbers can be made with the help of the digits 0, 1, 2, 3, 4, 5 which are greater than 3000 (repetition is not allowed)?

(a) 180

(b) 360

(c) 1380

(d) 1500

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**Ques.** The number of times the digit 5 will be written when listing the integers from 1 to 1000 is

(a) 271

(b) 272

(c) 300

(d) None of these

**Ques.** How many words can be made from the letters of the word INSURANCE, if all vowels come together?

(a) 18270

(b) 17280

(c) 12780

(d) None of these

**Ques.** In how many ways can 16 be divided into 4 person when none of them get less than 3

(a) 70

(b) 35

(c) 64

(d) 192

**Ques.** ^{n – 1}C_{3} + ^{n – 1}C_{4} > ^{n}C_{3}, then the value of *n* is

(a) 7

(b) < 7

(c) > 7

(d) None of these

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**Ques.** A person is permitted to select at least one and at most *n* coins from a collection of (2n + 1) distinct coins. If the total number of ways in which he can select coins is 255, then *n* equals

(a) 4

(b) 8

(c) 16

(d) 32

**Ques.** We are to form different words with the letters of the word INTEGER. Let m_{1} be the number of words in which I and N are never together and m_{2} be the number of words which begin with I and end with R, then m_{1} / m_{2} is equal to

(a) 30

(b) 60

(c) 90

(d) 180

**Ques.** Six ‘+’ and four ‘–’ signs are to placed in a straight line so that no two ‘–’ signs come together, then the total number of ways are

(a) 15

(b) 18

(c) 35

(d) 42

**Ques.** If ^{n}P_{5} = 9 x ^{n – 1}P_{4}, then the value of n is

(a) 6

(b) 8

(c) 5

(d) 9

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**Ques.** In a football championship, there were played 153 matches. Every team played one match with each other. The number of teams participating in the championship is

(a) 17

(b) 18

(c) 9

(d) 13

**Ques.** The number of ways in which first, second and third prizes can be given to 5 competitors is

(a) 10

(b) 60

(c) 15

(d) 125

**Ques.** In how many ways 3 letters can be posted in 4 letter-boxes, if all the letters are not posted in the same letter-box

(a) 63

(b) 60

(c) 77

(d) 81

**Ques.** How many numbers consisting of 5 digits can be formed in which the digits 3, 4 and 7 are used only once and the digit 5 is used twice?

(a) 30

(b) 60

(c) 45

(d) 90

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**Ques.** In how many ways can 10 true-false questions be replied

(a) 20

(b) 100

(c) 512

(d) 1024

**Ques.** The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is

(a) 420

(b) 840

(c) 2520

(d) 5040

**Ques.** In how many ways can 15 members of a council sit along a circular table, when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side

(a) 2 x 12!

(b) 24

(c) 2 x 15!

(d) None of these

**Ques.** How many numbers lying between 999 and 10000 can be formed with the help of the digit 0,2,3,6,7,8 when the digits are not to be repeated?

(a) 100

(b) 200

(c) 300

(d) 400

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**Ques.** Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

(a) 69760

(b) 30240

(c) 99748

(d) None of these

**Ques.** Number of divisors of n = 38808 (except 1 and *n*) is

(a) 70

(b) 68

(c) 72

(d) 74

**Ques.** How many different nine-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits occupy even places?

(a) 16

(b) 36

(c) 60

(d) 180

**Ques.** The greatest possible number of points of intersection of 8 straight lines and 4 circles is

(a) 32

(b) 64

(c) 76

(d) 104

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**Ques.** The exponent of 3 in 100 ! is

(a) 33

(b) 44

(c) 48

(d) 52

**Ques.** The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

(a) 6

(b) 18

(c) 12

(d) 9

**Ques.** The number of ways in which an arrangement of 4 letters of the word ‘PROPORTION’ can be made is

(a) 700

(b) 750

(c) 758

(d) 800

**Ques.** The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains at least 3 ladies is

(a) 252

(b) 672

(c) 444

(d) 420

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**Ques.** In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman

(a) 186

(b) 246

(c) 252

(d) None of these

**Ques.** Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done if the group is to have a majority of boys

(a) 120

(b) 90

(c) 100

(d) 80

**Ques.** The number of positive integral solutions of a b c = 30 is

(a) 30

(b) 27

(c) 8

(d) None of these

**Ques.** If the letters of the word *SACHIN* arranged in all possible ways and these words are written out as in dictionary, then the word *SACHIN* appears at serial number

(a) 603

(b) 602

(c) 601

(d) 600

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**Ques.** The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two female are not seated together is

(a) 480

(b) 600

(c) 720

(d) 840

**Ques.** How many words can be made from the letters of the word DELHI, if L comes in the middle in every word?

(a) 12

(b) 24

(c) 60

(d) 6

**Ques.** If a man and his wife enter in a bus, in which five seats are vacant, then the number of different ways in which they can be seated is

(a) 2

(b) 5

(c) 20

(d) 40

**Ques.** The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all at a time is

(a) 18

(b) 432

(c) 108

(d) 144

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**Ques.** In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct, is

(a) 11

(b) 12

(c) 27

(d) 63

**Ques.** The numbers of arrangements of the letters of the word SALOON, if the two O’s do not come together, is

(a) 360

(b) 720

(c) 240

(d) 120

**Ques.** Out of 10 white, 9 black and 7 red balls, the number of ways in which selection of one or more balls can be made, is

(a) 881

(b) 891

(c) 879

(d) 892

**Ques.** A question paper is divided into two parts A and B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is

(a) 80

(b) 100

(c) 200

(d) None of these

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**Ques.** In an election there are 5 candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote

(a) 125

(b) 60

(c) 10

(d) 25

**Ques.** There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that a ball does not go to box of its own colour is

(a) 8

(b) 7

(c) 9

(d) None of these

**Ques.** The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels do not occur together is

(a) 1200

(b) 2400

(c) 14400

(d) None of these

**Ques.** The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

(a) 360

(b) 900

(c) 1260

(d) 1620

**Ques.** A five digit number divisible by 3 has to formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

(a) 216

(b) 240

(c) 600

(d) 3125

**Ques.** There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is

(a) 6

(b) 11

(c) 13

(d) None of these