I realise this isn't the point of your post, but it's exceedingly unlikely that they all take vacations on different weeks... like 4.73 * 10^-22 unlikely if vac

I realise this isn't the point of your post, but it's exceedingly unlikely that they all take vacations on different weeks... like 4.73 * 10^-22 unlikely if vacation choice was random, which it isn't.