Problem Solving

1. in how many ways can a committee of 2 boys and 3 girls can be made out of 5 boys and 6 girls?


2.there are 4 copies of 5 different books. in how many ways can they be arranged on a shelf?

3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?

4. in how many ways can the letters of the word "missisippi" be arranged?


sorry guys i'm very bad at permutations and combinations... instead of just providing something like 7*6*5*4*3 can someone explain why they do it that way?

thanks for all of your help

fangtray wrote:
3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?

9*8*7

Anurag@Gurome wrote:

There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?

4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]

I thought the question asks all books arrangement, and got the answer 20!

LalaB wrote:

fangtray wrote:
3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?

9*8*7

thats what i thought at first. but its actually 9^3 ways. at least thats what is on the answer key. does somebody know?

fangtray wrote:

LalaB wrote:

fangtray wrote:
3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?

9*8*7

thats what i thought at first. but its actually 9^3 ways. at least thats what is on the answer key. does somebody know?

It cant be 9^3..
The first digit can be filled by any number from 1-9...9 ways
the scond digit can be filled by any number EXCEPT the number chosen for the first digit..hence, 8 ways
similarly, for the 3rd digit, it has to be filled in 7 ways ( coz 2 numbers are already chosen).
total ways : 9*8*7

had it been that the number can be chosen with repetation too, then it would have been 9*9*9..

Anurag@Gurome wrote:

There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?

4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]

why divide by 4!)^5?

fangtray wrote:

Anurag@Gurome wrote:

There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?

4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]

why divide by 4!)^5?

I believe that is necessary to avoid repetition. It is like the missippii problem posted by you.
The four copies are identical. Since there are 5 different books each book has 4 copies, we divide
by 4!^5