I remember reading this excellent little book with very easy to understand explanations of some of the basics re. permutations and combinations, back in school:<p>"Mathematics of Choice: How to Count Without Counting" by Ivan Morton Niven<p><a href="https://www.amazon.com/Mathematics-Choice-New-Mathematical-Library/dp/0883856158/ref=pd_cp_14_1?_encoding=UTF8&pd_rd_i=0883856158&pd_rd_r=NX2V9T7N5S5RHQ8K8ZFY&pd_rd_w=Swegj&pd_rd_wg=7p3Io&psc=1&refRID=NX2V9T7N5S5RHQ8K8ZFY" rel="nofollow">https://www.amazon.com/Mathematics-Choice-New-Mathematical-L...</a>
Why do we need this? What's wrong with good old "there are n ways to pick first element, n-1 ways to pick second, etc and then apply burnside to glue together things that we treat as identical"?