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2. (a) (10 points) On a shelf there are 5 different Japanese books, 6 different

ID: 3198895 • Letter: 2

Question

2. (a) (10 points) On a shelf there are 5 different Japanese books, 6 different Swahili books, and 8 different Sanskrit books. How many different ways are there to pick two books which are not both in the same language? (b) (10 points) How many different rectangles can be drawn on an 8 x 8 chessboard? Each rectangle can have height and width (which may differ) of 1 through 8 squares, aud two rectaugles are different if the subsets of chessboard squares that they cach contain are not exactly the samc.

Explanation / Answer

(b) in chessboard of 8*8 there are 9 horizontal and 9 vertical lines

A rectangle is formed by two horizontal lines and 2 vertical lines. How many ways can you choose two vertical lines? Well there are 9 total. So 9c2. Order doesn't matter, which is why we use combinations . This equals 36.

How many ways can you choose two horizontal lines. There are 9c2. Again order doesn't matter, so we use combinations. It equals 36 again.

36 * 36 = 1296

(a) 1st case one book is from Japanese and other is from Swahili

5c1*6c1= 30

2nd case one book is from Swahili and other from sanskrit

6c1*8c1=48

3rd case one book from Japanese and other book from sanskrit

5c1*8c1=40

Total ways =30+48+40

=118