Permutations and Combinations

1. In how many ways can you arrange PAJERO so that the vowels occupy alternate positions?

(a) 36 (b) 72 (c) 60 (d) 120

2. How many numbers greater than a million can be formed with the digits 4, 5, 5, 0, 4, 5, 3?

(a) 420 (b) 380 (c) 240 (d) 360

3. A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong envelopes?

(a) 119 (b) 120 (c) 720 (d) 719

4. Find the total number of numbers divisible by 2 which can be formed with the six digits 1, 2, 4, 5, 6, 7(with no digit repeated)?

(a) 260 (b) 460 (c) 220 (d) 360

5. How many 4 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) 40 (b) 400 (c) 5040 (d) 2520

6. In how many ways can the letters of the word ‘MACHINE’ be arranged so that the vowels may occupy only odd positions?

(a) 4 x 7 (b) 576 (c) 288 (d) none

7. The number of positive integers greater than 6000 and less than 7000 which are divisible by 5, with no digit repeated is

a) 28 b) 56 c) 112 d) 84

8. Find the probability of two ‘I’ are together when the letters of the word ‘UNIVERSITY’ is subjected to random arrangement.

a) 0.5 b) c) d) 0.2

9. In a symposium, four speakers – an economist, a politician, a union leader and a social worker, are to speak one after another. How many schedules showing the order in which these persons speak will have the economist speaking always after the politician?

(a) 6 (b) 12 (c) 24 (d) None of these

10. How many words can be formed using all the letters of the word ‘LAUGHTER’ so that the vowels are never together?

(a) 14400 (b) 3600 (c) 40320 (d) 36000

11. In how many ways a committee of 5 members can be selected for 6 men and 5 women consisting of 3 men and 2 women?

(a) 200 (b) 150 (c) 300 (d) 250

12. There are 12 points out of which 7 points are marked on the straight line. How many triangles is it possible to form?

a) 185 b) 175 c) 7! × 5! d) 140

13. If there are twelve persons in a party and if each two of them shake hands with each other, how many hand shakes happen in the party?

(a) 66 (b) 55 (c) 24 (d) 48

14. How many different Barbie’s can I make if I can choose from 4 different skin colours, 3 different eye colours, 4 different hairstyles and 6 different hair colors?

(a) 17 (b) 288 (c) 2488320 (d) None of these

15. 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) 194 (c) 205 (d) 209

16. A polygon has 44 diagonals. Find the number of sides?

(a) 44 (b) 22 (c) 11 (d) none of these

17. The sum of all the numbers which can be formed by using the digits 1, 2, 3, 4 all at a time (no digit is being repeated) is

(a) 10000 (b) 60000 (c) 66000 (d) 66660

18. In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?

(a) 3990 (b) 1540 (c) 1995 (d) 3672

19. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw?

(a) 32 (b) 48 (c) 64 (d) 96

20. A committee of seven is to be formed from 9 boys and 5 girls. In how many ways can this be done, when a committee contains at least three girls?

(a) 1726 (b) 1716 (c) 1617 (d) 2617

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