Permutation and Combination

Permutation and Combination-Exercise Questions

1. Evaluate 50!

                47!

a. 102500

b. 112584

c. 117600

d. 118450

2. Find the value of 85P3 .

a. 565350

b. 595650

c. 535950

d. 565350

3. Find the value of (20C18)*(20C20)

a. 400

b. 380

c. 360

d. 350

4. How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once?

a. 700

b. 720

c. 750

d. 800

5. There are 28 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?

a. 800

b. 820

c. 850

d. 870

6. In how many ways can the letters of the word, ‘TECHNOLOGY’ be arranged?

a. 1804400

b. 1814400

c. 1714400

d. 1704400

7. A bag contains 2 yellow balls, 3 white balls and 5 red balls. In how many ways can two balls be drawn from the bag?

a. 2C2

b.10C2

c.8C2

d.5C2

8. In how many ways can the letters of the word, ‘LANGUAGE’ be arranged in such a way that the vowels always come together?

a. 600

b. 700

c. 720

d. 750

9. In how many ways can the letters of the word, ‘KEYBOARD’ be arranged in such a way that the vowels always come together?

a. 4250

b. 4520

c. 4320

d. 4230

10. In how many ways can a team 16 be chosen out of a batch of 20 players?

a. 4845

b. 6852

c. 3125

d. 5846

11. How many ways can the letters of the word, ‘MACHINE’ be arranged so that the vowels may occupy only the odd positions?

a. 210

b. 576

c.144

d. 456

12. From a group of 5men and 4 women, 3 persons are to be selected to form a committee so that at least 2 men are there are on the committee. In how many ways can it be done?

a. 20

b. 50

c. 65

d. 86            

                                             

13. In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 9 women?

a. 7C4  9C5

b. 4C7  5C9

c. 7C5  9C4

d. 9C4  7C5

14. In how many ways can 5 boys and 3 girls sit around a table in such a way that no two girls sit together?

a. 1000

b. 1400

c.1440

d. 1800

Directions for questions 15 to 16:  Refer the data below and answer the questions below:

A letter lock has 3 rings each containing 6 letters.

15. What is the maximum number of false trials that can be made before the lock is opened?

a. 3*26C6

b. (26C6)3

c. 26C6. 3!

d. 215

16. How many such three letter passwords can exist?

a. 216

b. 26C6 *3

c. (26C6)3

d. (26C6)3 *63

17. How many different words can be formed from the word DAUGHTER so that ending and beginning letters are consonants?

a. 7200

b. 14400

c. 360

d. 1440

18. Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?

a. 1050

b. 25200

c. 32400

d. 5800

19. A box contains 3 white balls, 4 black balls and 5 yellow balls. In how many ways can 4 balls be drawn from the box, if at least one yellow ball is to be included in the draw?

a. 652

b. 547

c.425

d. 356

20. In how many ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?

a. 4586

b. 5896

c. 2415

d. 1771