Product carousel – how to present variants of a product?

I'm working on a product carousel for an e-commerce site.

I have a list of elements of one tile:

• Price
• Crossed price
• Badge/ribbon
• Image
• Caption (Product’s name)
• CTA (i.e. Show) as a button
• Ratings/Reviews (stars, number of stars, grey if none)
• Thumbnails (optional)
• Availability in stock
• Button, i.e. “More details”

Question: Let's say that we have a T-shirt available in 5 different colours. How can it be shown on product carousel on home page?

I thought about showing some colours block under the picture of a product. If doing so: How many of such colour blocks would be ok?

Second idea is to change the picture on a carousel randomly. It means: User goes on my page and sees blue T-shirt (maybe with colour blocks under the pic) among other products in product carousel. After reloading the page there will be a white T-shirt in carousel (maybe with colour blocks under the pic).

What would you recommend? What is the best way to show in product carousel that we have more colours on stock?