Permutation and Combination 1

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Subject: Permutation and Combination 1

Part 1: List for questions and answers of Permutation & Combination

 

Q1. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

a) 24400

b) 21300

c) 210

d) 25200

 

Q2. 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?

a) 159

b) 209

c) 201

d) 212

 

Q3. 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?

a) 624

b) 702

c) 756

d) 812

 

Q4. In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?

a) 610

b) 720

c) 825

d) 920

 

Q5. In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?

a) 47200

b) 48000

c) 42000

d) 50400 

 

Q6. 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?

a) 1

b) 126

c) 63

d) 64

 

Q7. In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged such that the vowels must always come together?

a) 9800

b) 100020

c) 120960

d) 140020

 

Q8. 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?

a) 10420

b) 11

c) 11760

d) None of these

 

Q9. 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?

a) 720

b) 420

c) 5040

d) None of these

 

Q10. In how many different ways can the letters of the word ‘LEADING’ be arranged such that the vowels should always come together?

a) 122

b) 720

c) 420

d) None of these

 

Q11. A coin is tossed 3 times. Find out the number of possible outcomes.

a) 8

b) 2

c) 1

d) None of these 

 

Q12. In how many different ways can the letters of the word ‘DETAIL’ be arranged such that the vowels must occupy only the odd positions?

a) 64

b) 120

c) 36

d) None of these

 

Q13. 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?

a) 64

b) 128

c) 32

d) None of these

 

Q14. In how many different ways can the letters of the word ‘JUDGE’ be arranged such that the vowels always come together?

a) 48

b) 32

c) 64

d) None of these

 

Q15. In how many ways can the letters of the word ‘LEADER’ be arranged?

a) 120

b) 360

c) 720

d) None of these

 

Q16. How many words can be formed by using all letters of the word ‘BIHAR’?

a) 720

b) 24

c) 120

d) 60

 

Q17. How many arrangements can be made out of the letters of the word ‘ENGINEERING’ ?

a) 924000

b) 277200

c) 182000

d) None of these 

 

Q18. 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?

a) 20

b) 16

c) 8

d) 24

 

Q19. In how many different ways can the letters of the word ‘RUMOUR’ be arranged?

a) 128

b) 360

c) 180

d) None of these

 

Q20. How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?

a) 720

b) 360

c) 1420

d) 1680 

 

Part 1: List for questions and answers of Permutation & Combination

 

Q1. Answer: d

Q2. Answer: b

Q3. Answer: c

Q4. Answer: b

Q5. Answer: d

Q6. Answer: c

Q7. Answer: c

Q8. Answer: c

Q9. Answer: a

Q10. Answer: b

Q11. Answer: a

Q12. Answer: c

Q13. Answer: a

Q14. Answer: b

Q15. Answer: c

Q16. Answer: c

Q17. Answer: b

Q18. Answer: a

Q19. Answer: c

Q20. Answer: d