# IOE Preparation Questions of Permutation & Combination

## IOE Preprration Questions of Permutation and Combination

### Quiz

- Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
- 25200
- 21300
- 24400
- 210

- In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
- 212
- 209
- 159
- 201

- 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 in the committee. In how many ways can it be done?
- 702
- 624
- 756
- 812

- In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
- 920
- 825
- 720
- 610

- In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
- 42000
- 48000
- 50400
- 47200

- In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
- 65
- 1
- 126
- 63

- In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
- 100020
- 140020
- 9800
- 120960

- There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
- 11
- 11760
- 10420
- None of these

- How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
- 5040
- 720
- 420
- None of these

- In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
- 720
- 420
- None of these
- 122

- A coin is tossed 3 times. Find out the number of possible outcomes.
- None of these
- 2
- 8
- 1

- In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
- 36
- None of these
- 64
- 120

- A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?
- 64
- 32
- None of these
- 128

- In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?
- None of these
- 32
- 48
- 64

- In how many ways can the letters of the word 'LEADER' be arranged?
- 360
- 720
- 120
- None of these

- How many words can be formed by using all letters of the word 'BIHAR'?
- 720
- 24
- 120
- 60

- How many arrangements can be made out of the letters of the word 'ENGINEERING' ?
- 782000
- 277200
- None of these
- 924000

- How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
- 24
- 16
- 8
- 20

- How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?
- 120
- 720
- None of these
- 24

- What is the value of 100P2 ?
- 12000
- 5600
- 9900
- 9801

- In how many different ways can the letters of the word 'RUMOUR' be arranged?
- 128
- None of these
- 360
- 180

- There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
- 3200
- None of these
- 1800
- 3600

- How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
- 720
- 1420
- 360
- 1680

- An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
- 110
- 100
- 64
- 80

- 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
- 600
- 625
- 576
- None of these

- A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?
- 48
- 12
- 24
- 62

- A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?
- 6020
- 9450
- None of these
- 1200

- In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
- 1200
- 1400
- 2880
- 3212

- Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
- 120
- 729
- 125
- 720

- In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
- 720
- None of these
- 120
- 60

- How many two digit numbers can be generated using the digits 1,2,3,4 without repeating any digit?
- 10
- 12
- 4
- 16

- There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
- 8
- 10
- 12
- 14

- There are 10 women and 15 men in an office. In how many ways can a person can be selected?
- 25
- None of these
- 150
- 50

- There are 10 women and 15 men in an office. In how many ways a team of a man and a woman can be selected?
- None of these
- 150
- 50
- 25

- In how many ways can three boys can be seated on five chairs?
- 80
- 60
- 30
- 120

- There are 6 persons in an office. A group consisting of 3 persons has to be formed. In how many ways can the group be formed?
- 10
- 60
- 30
- 120

- There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in a row. Find out the number of different arrangements possible.
- 25230
- 23420
- 21200
- 27720

- In how many ways can 7 boys be seated in a circular order?
- 120
- 720
- 5040
- 60

- In how many ways can 7 beads can be arranged to form a necklace?
- 360
- 120
- 720
- 60

- In how many ways can a team of 5 persons be formed out of a total of 10 persons such that two particular persons should be included in each team?
- 56
- 120
- 28
- 112

- In how many ways can a team of 5 persons be formed out of a total of 10 persons such that two particular persons should not be included in any team?
- 112
- 128
- 56
- 28

- How many triangles can be formed by joining the vertices of an octagon?
- 28
- 120
- 56
- 112

- If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
- 1024
- 64
- 1296
- 920

- Find the number of diagonals of a decagon?
- 12
- 28
- 35
- 16

- Find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?
- 360
- 120
- 480
- 240

- What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?
- 93024
- 91242
- 92314
- 93324

- In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
- 8
- 9
- 6
- 7

- There are 8 points in a plane out of which 3 are collinear. How many straight lines can be formed by joining them?
- 22
- 16
- 18
- 26

- How many quadrilaterals can be formed by joining the vertices of an octagon?
- 70
- 65
- 74
- 60

- How many straight lines can be formed by joining 12 points on a plane out of which no points are collinear?
- 66
- 62
- 72
- 58

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