Swapping Sweets

If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?
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Problem



Kate and Anna each have a bag that contains a red sweet, a blue sweet, a green sweet and a yellow sweet.

Without looking, Kate takes a sweet out of her bag and puts it into Anna's bag. Then, without looking, Anna takes a sweet from her bag and puts it into Kate's bag.

What is the probability that after this, each bag contains a red sweet, a blue sweet, a green sweet and a yellow sweet?

This problem is adapted from the World Mathematics Championships