To multiply fractions, we multiply the numerators together and the denominators together.

First, we will convert all the mixed numbers to improper fractions:

2 1/2 = 5/2
1 7/17 = 24/17

Now we have:

(5/2) x (24/17) x (7/12)

Multiplying the numerators:
5 x 24 x 7 = 840

Multiplying the denominators:
2 x 17 x 12 = 408

Therefore, the result is 840/408.

To simplify, we can divide both the numerator and the denominator by their greatest common factor, which is 12:

840 ÷ 12 = 70
408 ÷ 12 = 34

So, the simplified fraction is 70/34.