South Park Chef's Special!!

Chef decided to make some special muffins for South Park Elementary School's Thanksgiving celebrations. Each muffin would have a picture of one of the characters, made out of ready-to-roll coloured icing:

He found it much easier to make each picture in two halves: etc.

Unfortunately he asked Eric Cartman to help. He got the designs totally mixed up.

There were 5 designs, each had a top and a bottom.

Supposing Eric got it partly right and only had one top and one bottom on each muffin, how many different ways could he have placed the icing pictures (including the 5 correct ones pictured above.)

Supposing he got it totally wrong and could put 2 tops or 2 bottoms together. How many ways could he place the designs now?

Kenny came along to watch. Unfortunately Eric killed him (he thought he was one of the muffin tops waiting to be cut!). Stan told him not to use Kenny pictures in case it upset Kenny's mom. How many ways could Eric put the designs on now?

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