1. A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed? **(4)**

- (1) 56
- (2) 27
- (3) 26
- (4) 41
- (5) None of these

2. In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other? **(3)**

- (1) 5040
- (2) 240
- (3) 480
- (4) 720
- (5) None of these

3. In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? **(3)**

- (1) 10080
- (2) 4989600
- (3) 120960
- (4) 12960
- (5) None of these

4. There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is **(1)**

- (1) 24
- (2) 36
- (3) 40
- (4) 48
- (5) None of these

5. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by **(1)**

- (1) 6 ! × 5 !
- (2) 5 ! × 4 !
- (3) 30
- (4) 7 ! × 5 !
- (5) None of these