1. The problem statement, all variables and given/known data You have 10 pieces of fruits of which 1 is an orange, 1 is an apple, 1 is a pear, and 1 is a peach. How many ways are there to organize them in a row if the apples and oranges must be together and the pears and peaches cannot be together. 2. Relevant equations Mostly factorials 3. The attempt at a solution Total permutations = 10! Ways oranges and apples are together = 2!9! Ways peaches and pears cannot be together = 10! - 2!9! Unfortunately, I did not know how to combine them so in a futile attempt to get credit I stated: (10! - 2!9! + 2!9!)/(2!2!) = 10!/4 I am darn sure this is wrong. Could somebody enlighten me for the next time?