Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. in how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

Selecting 5 books out of 10 (8small, and 1large, and at most, only 1 large book.

Possible selections,

5 small books from overall 8, and no large book from overall 2

4 small books from overall 8, and 1 large book from overall 2

therefore, (8C5) + (8C4 x 2C1) = 196 ways.