Kaboobly Dooists visit the Canteen

Last Sunday, I had a $50 food coupon.

  • With it I could buy items from the canteen which costs at most $50.

  • I saw that I was so hungry that I had to buy exactly 5 items from the canteen.

  • However, the canteen had a strange rule. They partitioned their list of items in 2-tuples. You can only order at most one item from each tuple.

If the following is the list of the items labelled 'A' thru 'T' with the tuples contained in braces, in how many ways can I order the items?

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
[{'A': 12, 'B': 7},
{'C': 10, 'D': 9},
{'E': 7, 'F': 13},
{'G': 11, 'H': 9},
{'I': 8, 'J': 13},
{'K': 10, 'L': 10},
{'M': 8, 'N': 11},
{'O': 11, 'P': 9},
{'Q': 7, 'R': 11},
{'S': 9, 'T': 12}]

Image updated by Calvin
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