Mini-Sudoku

How many ways are there of completing the mini-sudoku?
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Problem

Image
Mini-Sudoku
 

A mini-sudoku is a 4 by 4 grid, where each row, column and 2 by 2 outlined block contains the digits 1, 2, 3 and 4 once and once only.

How many different ways are there of completing the mini-sudoku shown?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.