How often does the option to combine a robots.txt disallow with a robots.txt noindex statement make folders or URLs appear in SERPs?

Combining a robots.txt disallow with a robots.txt noindex statement will never make folders or URLs appear in SERPs. The Disallow directive in robots.txt prevents search engine crawlers from accessing a specific URL or directory. However, it doesn't prevent that URL from being indexed if it's linked from other pages. To explicitly prevent indexing, a noindex directive is needed. The crucial point is that if a page is disallowed by robots.txt, crawlers cannot access it to read the noindex meta tag or HTTP header. Therefore, the noindex directive cannot be discovered or honored. The page might still appear in SERPs if it's linked to, but it won't be indexed if the noindex is successfully read. Since Disallow prevents reading noindex, the combination is ineffective for preventing indexing.