Problem Solving

Hey folks..am back with doubts abt how to solve more permutation problems..
Hope these questions also act as a good revision for those who are looking for more qns in this topic.

Qn1. How many even number of 4 digits can be formed with the figures 3,4,7,8 if repetitions are allowed?
4 and 8 are even numbers in the n no.of digits available(3,4,7,8). To form an even number, the number will have to end with 4 or 8. So, to select the last digit (the formula would be 2P2) and to select the remaining 3 digits the formula would be 3P3. The final answer IMO would be 2P2 * 3P3.
Actual answer: 128

Qn2. How many numbers greater than 4000 can be formed from the figures 3,5,7,8,9 ? (repetitions not allowed)?
Clueless on this one. But this is my understanding of the question: Numbs greater than 4000 mean the permutation would include number from 5378 to 98753. So will have to figure out how many are these?
Actual answer: 216

Qn3. 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.
My understanding of this question:
(2n+2)Pn: (2n)Pn = 14:15
(2n+2)!/(2n+2-n) : (2n)!/(2n-n)!
(2n+2)!/(n+2)! : (2n)!/n! = 14 : 15
After this step, how to continue solving??
Actual answer:[spoiler] n = 3[/spoiler]

Qn 4. 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 ?
IMO:
the minimum num of digits that can be between 1 and 2 is only 1 digit.
Step 1:So, we would have to pick 1 digit out of the remaining 5 digits - 5P1
Step 2: Now that we have picked 1,2 and the digit inbetween 1 and 2, we need to find remaining number of 4 digits. For this, 4P4
Step 3: Treat 1, 2 and the digit in between 1 and 2 as one unit. SO we have remainig 4 units. So total, 5 units - 5P5
Step 4: Multiply: 5P1 * 4P4 * 5P5 = 14400
Actual answer: 15

Qn 5. In how many ways can 5 different mathematics books, 4 different physics books and 2 different chemistry books be arranged on a shelf if the books in each subject are to be together.
IMO:
Since each subject books will have to be together treat as 3 units instead of 5+4+2=11 units. So, 3P3
Now among the 5 math book there are difft wayts of arrangement : 5P5. Same goes for physics and chemisttry books.
Therefore IMO answer shd be 3P3 * 5P5 * 4P4 * 2P2 = 28800
Actual answer: 34560

Qn 6. Find the number of arrangements of the letter in the word PENCILS if (i) E precedes I, (ii) there are three letters between E and I.
Actual answer : (i) 2520 (ii) 120

Qn 7. 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 ?
I thought this was a fairly simple question! There are 9 letters in the word PRINCIPLE. So IMO 9P9 is the answer.
Actual answer: 90720

Qn 8. In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
Actual answer: 181440

Qn 9. 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?
Actual answer: (i) 141120 (ii) 20160

Qn 10. How many different arrangements of the letters in TOMATO are there, if the letters O are to be separated?
Actual answer: 120

Qn 11. 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?
2 particular people must sit in the back seat and 1 particular person is the driver. therefore, only remaining 2 pple are left to be seated in the back seat and so, out of 7 choices, we only have 4 choices. So, 4P2.
1 particular person is the driver, so there are 3 pple that we need to select from the remaining 3 pple. So, 3P3
Multiple 4P2 * 3P3
Actual answer: 288