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Sep 21, 2022 at 23:41 comment added user2661923 @MeTAZOIS Did you find my answer educational?
Sep 21, 2022 at 23:40 comment added MeTAZOIS Thanks for answering first, but I don't think this much level of details is involved in this problem.
Sep 21, 2022 at 23:06 comment added user2661923 @JMoravitz For the math student new to Combinatorics, detailing a more elegant approach is, in my opinion, cart before the horse. It is better to start with a deep understanding of what is going on, before striving for elegance.
Sep 21, 2022 at 23:04 comment added user2661923 @JMoravitz Different opinions make a horse race. The point of my answer is not to show the best way of attacking the problem. The original poster showed, in his posting, confusion over basic enumeration concepts. As I remarked at the start of my answer, I specifically detailed the more difficult way, precisely because it is more educational. The original poster is (in effect) drilled in the concepts of mutually exclusive partition patterns, suit-factors, and combination-factors. If I was writing a textbook, this is how I would educate the student. ...see next comment
Sep 21, 2022 at 23:01 comment added JMoravitz Although your answer is not incorrect, I do find it irresponsible to be promoting an approach by casework to this level. Especially when the problem has an elementary approach that avoids it entirely.
Sep 21, 2022 at 22:53 history answered user2661923 CC BY-SA 4.0