1. The problem statement, all variables and given/known data There are 15 different apples and 10 different pears. How many ways are there for Jack to pick an apple or a pear and then for Jill to pick an apple and a pear? 2. Relevant equations 3. The attempt at a solution Let apples be A and pears P. Since Jack chooses either an apple or pear, he has 25 possibilities. This leaves Jill to choose a pair from either: 14A, 10P or 15A, 9P So Jill's choices = 25[14(10) + 15(9)] = 6875 Which is rather far from the given answer of 15[10(14 + 9)] = 3450 and I do not see how this was arrived at. What am I doing wrong here?