Random coupling of halides

You will predict the products of coupling several halides at random with sodium. You will count the products, find the share of each, and work out how much sodium is needed.

The idea. With $k$ different halides, the coupling gives $k(k+1)/2$ products, because each pair counts once and each halide can also couple with itself. A random pair of halide molecules $i$ and $j$ has the probability $x_i x_j$, or twice that when $i$ and $j$ are different.

Your tasks.

1. Complete n_products(k).
2. Complete shares(amounts) so that it returns a dictionary from a product name, such as "Ar-R", to its percentage. The product name joins the two halide names in alphabetical order.
3. Complete sodium(amounts), the amount of sodium in mol, with one sodium atom for each halide molecule.