Hi, I was answering what I thought was an easy problem and I got it wrong, but not sure why. Please give me an insight.(adsbygoogle = window.adsbygoogle || []).push({});

Problem: 12 juniors are ordered (in a line) for a drill. What's the probability (assuming all arrangments are random) of Dave standing next to Beth?

My reasoning: There are 12! possible arrangments of juniors. The number of arrangments where Dave is next to Beth is 2 (number of ways Beth can stand next to Dave, DB - BD) multiply by all possible arrangments for the remaning juniors, i.e. 10!. So, the probability is then 2x10! / 12!.

Well, that's wrong - 2 must be multiplied by 11!, not 10!, but I don't understand why - there are 10 juniors left to be ordered in any way to be combined with Beth and Dave. I realize that if I write it out on a paper, I'll count 11! of them. But I don't want to simply memorize the formula for this type of problem, I want understand the reasoning. Why 11! ?

Thanks,

Pavel.

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# Permutations and arranging order

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