SOLUTION: A student has to sell 2 books from a collection 25 biology, 21 mathematics, and 14 chemistry books. How many choices are possible if: a. both books are to be on the same sub

25 biology books Choose 2        <-- 25C2 ways
      or                             plus
21 mathematics books Choose 2    <-- 21C2 ways
      or                             plus 
14 chemistry books Choose 2      <-- 14C2 ways
      
25C2 + 21C2 + 14C2 = 300 + 210 + 91 = 601 ways.

Case 1:  Choose a biology book and a mathematics book.

Choose the biology book any of 25 ways.
Choose the mathematics book any of 21 ways.
That's (25)(21) ways.

Plus

Case 2:  Choose a biology book and a chemistry book.

Choose the biology book any of 25 ways.
Choose the chemistry book any of 14 ways.
That's (25)(14) ways.

Plus

Case 3:  Choose a mathematics book and a chemistry book.

Choose the mathematics book any of 21 ways.
Choose the chemistry book any of 14 ways.
That's (21)(14) ways.

Answer:  (25)(21) + (25)(14) + (21)(14) = 525 + 350 + 294 = 1169 ways.

Edwin