(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Probability Midterm Question: Fruit row counting

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