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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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