Can I do random like this? How Pasan's way different from me?

You can use the arc4random_uniform as an alternative way to generate a random number; however, in addition to using a different method for generating a random number, Pasan is actually trying to get you to generate a random fact (String) as the return value, not just the index (he actually passes this value through as a part of the method itself). So, in order to achieve the same thing as the video — but while using your method instead of the GameKit random generator option — you'd want to:

struct FactProvider {

    let facts = [  "My first fact goes here",
                         "This is the second fact",
                         "A third fact can be placed here on this line",
                         "Fourth fact of the array goes here",
                         "I love facts"  ]

    // Arc4Random_uniform number generator
    func random(_ n:Int) -> String {
        return facts[Int(arc4random_uniform(UInt32(n)))]
    }

}

And in the view controller file, you'd instead add:

funFactLabel.text = factProvider.random(factProvider.facts.count)

The main reason for why you'd want to do this (generate an actual fact rather than simply an index value that you have to pass through) is that you can actually pass the final value around more easily, and this better achieves the DRY (Don't Repeat Yourself) principle by cutting down on the code required.

Hope this explains the difference a little better!!

I believe in the current version of Swift you can also do

Int.random(in: range)