Evaluate binomial coefficients

For a start, you can get the length of the corresponding list of combinations:

say combinations(5, 3).elems;

Output:

10

This method is efficient, as Raku will not actually compute each element of the list, since it actually uses an iterator with a defined count-only method. Such method performs computations in a way similar to the following infix operator:

sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. $^p }
say 5 choose 3;

A possible optimization would use a symmetry property of the binomial coefficient:

sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p) }

One drawback of this method is that it returns a Rat, not an Int. So we actually may want to enforce the conversion:

sub infix:<choose> { ([*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p)).Int }

And this is exactly what the count-only method does.