II. PERMUTATION I (LINEAR ARRANGEMENTS)
1. How many different arrangements can be made by taking 3 letters of the word SUNDAY ?
2. In how many ways can 5 boys be arranged in a row ?
3. In how many ways can a first, second and third prize be awarded in a class of 8 students ?
4. How many 5-digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once in a number ? How many even numbers can be formed ?
5. Find the value of (i) (ii) (iii)
6. Find the value of (i) 6! (ii) 8! / 5!
7. In how many ways can 4 consonants and 3 vowels be arranged in a row (a) so that the 3 vowels are always together, (b) so that the first and the last places are occupied by consonants.
7a. There are 4 different mathematics books, 6 different physics books, and 2 different chemistry books are to be arranged on a ****f. How many different arrangements are possible if (a) the books in each category must all stand together , (b) only the mathematics books must stand together.
8. In how many ways can four girls and three boys be arranged in a row so that (a) the boys are always together, (b) the girls and boys occupy alternate places ?
9. In how many ways can 6 people be seated in a motor car if only 2 can occupy the driver's position ?
10. In how many ways can 6 people be arranged in a circle if 2 particular people are always (a) together (b) separated.
11. Father, mother and 6 children stand in a ring. In how many ways can they be arranged if father and mother are not to stand together.
12. In how many ways can 5 boys and 3 women be arranged (a) in a row , (b) in a circle if both cases the women are always to stand together ?
13. Four men and four women are to be seated alternately (a) in a row (b) at a round table. In how many ways can this be done ?
14. How many even number of 4 digits can be forned with the figures 3,4,7,8 if (a) no figure is repeated , (b) repetitions are allowed.
15. How many numbers greater than 4000 can be formed from the figures 3,5,7,8,9 ? (repetitions not allowed).
16. In how many ways can the letters of the word PERMUTE be arranged if (i) the first and last places are occupied by consonants, (ii) the vowels and consonants occupy alternate places.
17. If , find r.
18. The number of arrangements of 2n+2 different objects taken n at a time is to the number of arrangements of 2n different objects taken n at a time as 14:15. Find the value of n.
19. How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if (i) the numbers begins with 1 and ends with 2, (ii) there are not more than 2 digits between 1 and 2 ?
20. If , find the value of n. 
21. In how many ways can 5 different mathematics books, 4 different physics books and 2 different chemistry books be arranged on a ****f if the books in each subject are to be together.
22. In how many can 3 men, 3 women and 3 boys be arranged in a row if the three boys are to remain together ?
23. Find the number of arrangements of the letter in the word PENCILS if (i) E is next to I, (ii) E precedes I, (iii) there are three letters between E and I.
24. In how many ways can the letters of the word PRINCIPLE be arranged? In what proportion of these arrangements do the letters P come together ? .
25. In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
26. How many arrangements can be made by the letters of word DEFINITION (i) if the letters I do not occupy the first or last place, (ii) if the letters I are together?
27. How many different arrangements of the letters in TOMATO are there, if the letters O are to be separated?
28. A car can hold 3 people in the front seat and 4 in the back seat. In how many ways can 7 people be seated in the car if 2 particular people must sit in the back seat and 1 particular person is the driver?
29. In how many ways can 4 people be accommodated if there are 4 rooms available?
30. In how many ways can 8 oarsmen be seated in a eight-oared boat if 3 can row only on the stroke side and 3 can row only on the bow side ?
31. Prove that (i) from the definition of .
(ii) the formula for that .
32. Prove that .
33. In how many ways can 5 men and 5 women by arranged in a circle so that the men are separated? In how many ways can this be done if two particular women must not be next to a particular men.
34. How many arrangements of the letters of the word PARRAMATTA are possible?
1. 120 2. 120 3. 336 4. 720; 360 5.(i) 120 (ii) 11800 (iii) 6720 6.(i) 720 (ii) 336
7.(a) 720 (b) 1440 7a (a) 207360 (b) 8709120 8.(a) 720 (b) 144 9. 240 10.(a) 120
(b) 48 (c) 72 11. 3600 12. (a) 4320 (b) 720 13.(a) 1152 (b) 144 14. (a) 12 (b) 128
15. 216 16 (i)1720 (ii) 72 17. r=3 18. 3 19.(i) 120 (ii) 15 20. 4 21. 34560 22. 30240
23. (i) 1440 (ii) 2520 (iii) 120 24. 90720, 22.2% 25. 181440; 1440 26. (i) 141120 (ii) 20160 27. 120 28. 288 29. 256 30. 1152 33. 2880; 864 34. 37800