5...Marie Curie, Linus Pauling, John Bardeen, Frederick Sangerand Nelson Mandela
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Between 1901 and 2011, the Nobel Prizes and the Prize in Economic Sciences were awarded 549 times.
Since the three prizes are the same, the answer is the number of combinations of 3 out of 80. That is 82160 ways.
Just one - 1921 Nobel prize (physics). Curiously, rather than receiving an award for his more famous work on relativity, he won it for his work on the photoelectric effect, which was responsible, in part at least, for the development of quantum theory. It is arguable that, given the work that had been done previously by the likes of, for example, Lorentz, relativity was a theory waiting to happen, whereas the photoelectric effect was much more novel and far-reaching in its effects.
I kind of depends, but 12 would be the answer I would suggest. Because; Then all 12 children can have 3 prizes and 2 balloons. It would be completely equal.
There are infinitely many of them: 168000168 for example.