(From Sheldon Ross, First course in probability – p. 17, problem 16)
A student has to sell 2 books from a collection of 6 math, 7 science and 4 economics books.
How many choices are possible if
(a) both books are to be on the same subject
(b) the books are to be on different subject?
Answer for part (b): There are 6⋅7 choices of a math and a science book, 6⋅4 choices of a math and an economics book, and 7⋅4 choices of a science and an economics book. Hence, there are 94 possible choices.
My logic is – 1 math book out of 6 can be selected in 6 ways and second book out of (7 science + 4 economics) in 11 ways, so total 66 OR 1 science book out of 7 in 7 ways and second book out of (6 math + 4 economics) in 10 ways, so total 70 ways OR 1 economics book out of 4 in 4 ways and second book out of ( 6 math + 7 science) in 13 ways, so total 52 ways, adding the 3 numbers we get total = 66 + 70 + 52 = 188.
Where am I going wrong?
Best Answer
You're counting everything twice. For example, you're counting math and science as math and science-or-economics, but you're also counting it as science and math-or-economics.