keeping different breeds together
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Yes, you can keep them all together, if you have a coop big enough for all. And partridge Brahmas are fairly easy to ses by 5 weeks. Just look at the chest feathers. Black chest feathers is a sure sign of a cockerel.
Your main issue, if you keep your boy is that you don't have enough females for him. A general guideline is about 8 to 10 hens per rooster. Some need more than that, and some a fine with fewer. But rooster 'damage' on the hens is a real problem when you only have 6 or 7 hens.
Why 3 separate coops? And what are the dimensions?