Permutation problems

[sjpre10]

Hello

For the followings questions I am getting confused while solving. Please give your views how to go through these type of problems. If possible solve the problems with proper explanation.

I will post answers later after some discussions as here answer solves the problem

1. In how many ways can 6 people be seated in a motor car if only 2 can occupy the driver's position ?

2. In how many ways can 6 people be arranged in a circle if 2 particular people are always (a) together (b) separated.

3. 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.

4. 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 ?

5. How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if there are not more than 2 digits between 1 and 2 ?

6. 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.

7. 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?

8. 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 ?

9. 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.

[Chlyxu]

answers please!!

[Brent Hanneson]

Please provide answer choices. Why? Some GMAT counting questions can be solved by eliminating incorrect answers.
Also, please limit yourself to 1 question per thread. Otherwise, we will have 9 separate conversations occurring at once.

Cheers
Brent