0
Short answer: 21
We can use combinatorics to solve this using the binomial coefficient to choose five elements out of a set of seven.
The equation for this is:
n!
------------
(n - k)! k!
Where n is the size of the set, k is the number of elements to choose, and "------------" is a crude attempt at a division sign.
In our case, n = 7, k = 5:
7!
------------
(7 - 5)! 5!
5040
------------
(2) (120)
5040
------------
240
5040 / 240 = 21
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