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You will have two formal evenings, but those that don't want the DJ and white shirt/bow tie could simply wear a smart suit for the gents and jacket and long trousers for the ladies. At a guess there will be others wearing similar attire but probably around 70% will be formal. Alternatively the ones who don't want the formal wear could go for a different venue for the meal on both nights and you meet up with them afterwards, but as you are only cruising for 7 nights it is really worth seeing, being first time cruisers. The main thing is relax and enjoy yourselves it should be a marvellous time for you all.
I would go with Blyth's answer & if you type formal into the blue search box you will see it is a much discussed subject on cruise ships & often can get quite heated. I would suggest you go with it & enjoy the atmosphere it can create.
I also agree that the majority of passengers will be dressed in a suit or a DJ in fact there will probably some dressed in the kilt for the two formal nights that leaves you with five other nights to be casually dressed. I think it would be a shame if you didn't try at least one formal night and then you will know for the other whether to opt out and use the informal restaurant. There is another major web-site where this matter will be discused but if I put it this message will not be published. ... Neil.
OK - this is how you get to the site that Neil refers to...Make sure that you sign up for the meet&mingle party that they throw. You go to royalcaribbean.co.uk >contact us> FAQs > and then under the On Board section it tells you how. You will have to register (it is free). It is a private party, the Captain attended our last one, and it is an excellant way to meet and converse with your fellow travellers before hand, and you can chat with them and find out the concensus on getting dolled up. Via the link that is provided in the royalcaribbean site you will find the 'site that cannot be named'. IMHO it would be a shame to go on a cruise and not partake in the 'dressing up' as that is part of it. On my last cruise over 95% were dressed up and those that were not stuck out like a sore thumb (and in my views looked rather embarrassed) Happy cruisin'.
Love the formal nights on a cruise only time we seem to get dressed up and really go for it. Bit like a parade of penguins sometimes but love it just the same.
Lets face it that's what cruising is all about, spoiling yourselves and enjoying yourselves and who the hell cares what others think as they are thinking the same as you