SOLUTION: Hi, Please help! There are 21 English books and 19 French Books. How can these books be arranged on a shelf where no 2 french books are placed together?

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Question 367067: Hi, Please help!
There are 21 English books and 19 French Books. How can these books be arranged on a shelf where no 2 french books are placed together?
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1 : we put between French books 1 English books, hence we now have 19+18 = 37 books.

Step 2 : we put the 3 remaining English books at any place, this makes : 38*39*40 possibilities but we have to get rid of the order, hence we get :

N = 38*39*40/6 = 38*13*20 = 260*38 = 9880 possibilities.