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 subject?
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.
b. the books are to be on different subjects?
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