Few more permutations/combination questions

1. In how many ways can 5 rings be worn on the four fingers of the right hand?

2. Three math books, four english books, and four reasoning books are kept on a shelf. In how many ways can they be arranged so that the books of each type are always together?

3. How many 3 letter words can be constructed using all the 26 letters of the english alphabet if only the middle letter of each word is a vowel?

4. In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together?

5. In how many ways can all the 7 sweets be distributed to three friends Jack, Jill, and John so that Jill alway sgets 2 sweets and each of them gets at least one sweet?

6. In how many ways can 4 men and 4 women sit at a round table with no two women in a consectuive position?

7. In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?

cans wrote:

1. In how many ways can 5 rings be worn on the four fingers of the right hand?

Assuming one finger can have all the 5 rings: 4^5. (4*4*4*4*4)

2. Three math books, four english books, and four reasoning books are kept on a shelf. In how many ways can they be arranged so that the books of each type are always together?

3!*3!*4!*4!

fangtray wrote:

cans wrote:

1. In how many ways can 5 rings be worn on the four fingers of the right hand?

Assuming one finger can have all the 5 rings: 4^5. (4*4*4*4*4)

2. Three math books, four english books, and four reasoning books are kept on a shelf. In how many ways can they be arranged so that the books of each type are always together?

3!*3!*4!*4!

why do you do that for #2? how do you come up with your answers ?

cans wrote:

4. In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together?

arrange 7 white balls: 1 way.
no. of gaps = 8
pick any 5 spaces and put black balls. 8C5.
Arrange them:1
thus 8C5

5. In how many ways can all the 7 sweets be distributed to three friends Jack, Jill, and John so that Jill alway sgets 2 sweets and each of them gets at least one sweet?

7C2 (for Jill) * (2^5 - 1 -1) (2^5 because each of the sweet can be given to any of the 2 persons.
-1 and -1 because in case all the sweets given to only Jack or to only John)