- #1
DrAlexMV
- 25
- 0
Homework Statement
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.
Homework Equations
Mostly factorials
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?