Permutation and Combination

Q. 16 persons are participating in a party. In how many different ways can they host the seat in a circular table if the 2 particular persons are to be seated on either side of the host?

1. 16! $\times$ 2
2. 14!
3. 14! $\times$ 2
4. 14! $\times$ 3
5. 18! $\times$ 2

Q. Find the number of women who like diamond only.

1. 60
2. 240
3. 120
4. 198
5. 84

Q. What is the difference between the total number of students who prefer beverages P and R together and the total number of students who prefer beverages S and V together?

1. 958
2. 953
3. 952
4. 957
5. None of these

Q. In an examination hall, there are 4 rows of chairs. Each row has 8 chairs 1 behind the other. There are 2 classes sitting for the examination with 16 students in each class. It is desired that in each row all students belong to the same class and that no 2 adjacent rows are allotted to the same class. In how many ways can these 12 students be seated?

1. None of these
2. $2\times 16!\times 16!$
3. $2\times 16!\times 15!$
4. $2\times 15!\times 15!$
5. $16!\times 16!$

Q. Find the number of women who like both diamond and emerald.

1. 32
2. 30
3. 24
4. 28
5. 27