HI all! THis is CowMIlk .

At the first of the class, we went over the homewoks

" In how many ways can 4 english books and 3 french books be arranged in a row on a shelf"

To solve this peoblem, we could use

or 7! = 5040 ways

Question b :

In how many ways will the french books are together:

At first we put 3 Fernch books in a bag, and find how many way can arrange this bag and 4 English books, It will = 5!. After that we find how many way 3 french books in the bag can arrange, which is 3! .So...we have 5! to arrange the bag and English books,3! to arrange the frech books in the bag=> the number of way to do both of this is 5! .3! = 720 ways.

Then , we learn the formula n!/(k1*k2*k....)

Where : n total ways to arrange

k the number of way overlap

Ex In the word BOOK , we have total ways to arrange is 4!

and we see 2" O " which could be repeat like this OO and OO

because it is the same word so we don't need it the number of way is 4!/2! = 12 ways

The same with the word MISSISSIPPI = 11!/(4!*4!*2!)= 34650 ways

That is all of the Importance point ( I think ^^)

Bye bye