How are StreetPass items rewarded?

In Animal Crossing: New Leaf, I've noticed that players that StreetPass with you more than once will give you handheld accessories when you visit them at the Happy Home Showcase. These items are handheld accessories... things like balloons and party favors.

Is there any order or pattern to how these are rewarded, or are they randomly selected from a pool of potential rewards with each new visit?

There is indeed a certain order in which you receive the items, up to a point. Afterwards, you receive one of the previously awarded items randomly. The order is as follows:

First time: Nothing
Second time:  Balloon
Third time:   Balloon
Fourth time:  Pinwheel
Fifth time:   Bunny Balloon
Sixth time:   Bubble Wand
Seventh time: Heart Balloon
Eighth time:  Ice Cream
Ninth time:   Soft-serve Ice Cream
Tenth time:   Party Blower
More than ten times: Random item listed above

The color of the items you receive is random. You also can only Streetpass the same person every 8 hours to receive these gifts.

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