var images = [UIImage(), UIImage(), UIImage(), UIImage(), UIImage()]

while images.count != 0 { // Ejecuta hasta que el array de imágenes está vacío

    let i = Int(arc4random_uniform(UInt32(images.count))) // Genera un aleatorio
    imageView.image = images[i] // asigna la imagen al imageView
    images.remove(at: i) // La elimina del array

}

var image1 = UIImage()
var image2 = UIImage()
var image3 = UIImage()
var image4 = UIImage()

// le asigno nombres para proposito
// de demostrarte el demo.
image1.accessibilityIdentifier = "image1"
image2.accessibilityIdentifier = "image2"
image3.accessibilityIdentifier = "image3"
image4.accessibilityIdentifier = "image4"

var images = Images(images: [image1, image2, image3, image4])

var randomImage1 = images.getRandomImageNotUsed()
var randomImage2 = images.getRandomImageNotUsed()
var randomImage3 = images.getRandomImageNotUsed()
var randomImage4 = images.getRandomImageNotUsed()

print(randomImage1?.accessibilityIdentifier)
print(randomImage2?.accessibilityIdentifier)
print(randomImage3?.accessibilityIdentifier)
print(randomImage4?.accessibilityIdentifier)

var randomImage5 = images.getRandomImageNotUsed()
print(randomImage5)

Optional("image1")
Optional("image3")
Optional("image4")
Optional("image2")
nil

Optional("image2")
Optional("image3")
Optional("image4")
Optional("image1")
nil

import UIKit

struct Images {
  private var images: [UIImage]
  private var unusedImageIndexes: [Int]

  init(images: [UIImage]) {
    self.images = images
    self.unusedImageIndexes = Array(0...images.count - 1)
  }

  mutating func getRandomImageNotUsed() -> UIImage? {
    if unusedImageIndexes.count > 0 {
      let randomValue = Int(arc4random_uniform(UInt32(unusedImageIndexes.count)))
      let randomIndex = unusedImageIndexes[randomValue]

      unusedImageIndexes.remove(at: randomValue)

      return images[randomIndex]
    } else {
      return nil
    }
  }
}