Permutation and Combination

1. In how many different ways, 4 boys and 2 girls can sit on a bench?
(a) 620         (b) 640
(c) 720       (d) None of these

2. A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men, 3 women and 1 child be selected from the given group?
(a) 600        (b) 300
(c) 900          (d) 750

3. Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
(a) 32          (b) 30
(c) 55            (d) 29

4. A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from this group?
(a) 300         (b) 600
(c) 450          (d) 750

5. In how many ways can 5 boys and 3 girls sit in a row such that all boys sit together?
(a) 3800        (b) 4760
(c) 2880      (d) 1401

6. The number of sequences in which 7 players can throw a ball so that the youngest player is not the last is:
(a) 2010           (b) 2120
(c) 4320        (d) 4322

7. A delegation of 5 members has to be formed from 3 women and 5 men. In how many ways the delegation can be formed, if 2 particular women are always included in the delegation?
(a) 20              (b) 54
(c) 40                (d) 32

8. How many new words can be formed by rearranging the letters of the word ‘ALIVE’?
(a) 24              (b) 23
(c) 119          (d) 120

9. In how many ways can 3 consonants and 2 vowels be selected from the letters of “TRIANGLE”?
(a) 25           (b) 30
(c) 35            (d) 40

10. In a class, there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
(a) 400           (b) 600
(c) 500         (d) 200

11. A question paper consists of 5 problems, each having 3 choices. In how many ways can a candidate attempt one or more problems?
(a) 632       (b) 1023
(c) 521        (d) 151

12. A letter lock consists of 3 rings, each marked with 6 different letters. The number of failed attempts to open the lock at the most can be:
(a) 216           (b) 243
(c) 215         (d) 729

13. How many 4-digit numbers can be formed using the digits {1, 3, 4, 5, 7,9} (repetition is not allowed)?
(a) 360       (b) 60
(c) 300         (d) 180

14. How many 4-digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}?
(a) 100         (b) 360
(c) 240         (d) 60

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

16. From a group of seven men and six 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?
(a) 650          (b) 756
(c) 762           (d) 763

17. 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) 830

18. In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?
(a) 50400        (b) 40500
(c) 30500           (d) 50320

19. In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
(a) 2880           (b) 1400
(c) 1600              (d) 1800

20. A question paper has 2 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?
(a) 8450            (b) 8451
(c) 9450         (d) None of these