Permutation and combination Practice Questions

Permutation and combination Practice Questions

1. In how many different ways can the numbers '256974' be arranged,   using   each   digit   only   once in each 21 arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?

(a) 48                 (b) 720               (c) 36                  (d) 360

(e) None of these

2. An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

If three marbles are drawn at random, what is the probability that at least one is yellow?

(a)                     (b)              (c)               (d)

(e) None of these

3. An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If two marbles are picked at random, what is the probability that both are green?

(a)                  (b)                   (c)                    (d) 1

(e)  None of these

4. An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

If two marbles are drawn at random, what is the probability that both are red or at least one is red?

(a)                 (b)                    (c)               (d)

(e) None of these

5. An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If three marbles are picked at random, what is the probability that two are blue and one is yellow?

(a)                  (b)                  (c)                  (d)

(e) None of these

6. An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If four marbles are picked at random, what is the probability that at least one is yellow?

(a)               (b)                 (c)                (d)

(e) None of these

7. In how many different ways can the letters of the word 'PRAISE' be arranged?

(a) 720               (b) 610               (c) 360               (d) 210

(e) None of these

8. An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

If three marbles are drawn at random, what is the probability that none is green?

(a)                    (b)               (c)                  (d)

(e) None of these

9. An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If four marbles are picked at random, what is the probability that at least one is yellow?

(a)                    (b)               (c)                    (d)

(e) None of these

10. On a shelf, there are 4 books of Economics, 3 books of 1 Management and 4 books of Statistics. In how many different ways, can the books be arranged so that the books of Economics are kept together?

(a) 967680        (b) 120960        (c) 5040             (d) 40320

(e) None of these

11. An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

If eight marbles are drawn at random, what is the probability that there are equal number of marbles of each colour?

(a)                   (b)               (c)             (d)

(e) None of these

12. In how many different ways can the letters of the word 'AWARE' be arranged?

(a) 150                (b) 120               (c) 40                  (d) 60

(e) None of these

13. An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

If four marbles are picked at random, what is the probability that one is green, two are blue and one is red?

(a)                  (b)              (c)                  (d)

(e) None of these

14. A committee of 6 teachers is to be formed out of 4 Science teachers, 5 Arts teachers and 3 Commerce teachers. In how many different ways can the committee be formed if

Two teachers from each stream are to be included ?

(a) 210                (b) 180               (c) 145                (d) 9

(e) None of these

15. An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

If four marbles are drawn at random, what is the probability that two are blue and two are red?

(a)             (b)                  (c)               (d)

(e) None of these

16. In how many ways 3 prizes can be given away to 7 boys, when each boy is eligible for any of the prizes?

(a) 7³                   (b) 3⁷                  (c) 7⁷                   (d) 3³

(e) 7³ – 3⁷

17. A committee of 6 teachers is to be formed out of 4 Science teachers, 5 Arts teachers and 3 Commerce teachers. In how many different ways can the committee be formed if No teacher from the Commerce stream is to be included ?

(a) 81                  (b) 62                 (c) 46                  (d) 84

(e) None of these

18. Two persons A and B appear in an interview for two different vacancies. If the probabilities of their selections are  and  respectively. Find the probability that none of them is selected.

(a)                 (b)                  (c)                    (d)

(e)

19. A committee of 6 teachers is to be formed out of 4 Science teachers, 5 Arts teachers and 3 Commerce teachers. In how many different ways can the committee be formed if

Any teacher can be included in the committee ?

(a) 626               (b) 718                (c) 924               (d) 844

(e) None of these

Answers:

1. a
2. b
3. e
4. e
5. c
6. b
7. a
8. e
9. b
10. a
11. c
12. d
13. c
14. b
15. a
16. a
17. d
18. d
19. c