Exercise: Implement a function combinations $($k$,$ elements$)$ implementing the function $C$ above, that is$,$ returning the set of $k-$elements subsets of elements.

Hint: the difficulty is not in writing the recursion, but in deciding when NOT to recur, and rather, yield a result or the absence of results.

Exercise: Generating Combinations

$1$ #@title Exercise: Generating Combinations

$2$

def combinations$($k$,$ elements$)$:

assert isinstance$($elements$,$ list$)$

# This can be done in $9$ lines of code, and possibly fewer.

### YOUR SOLUTION HERE

$(1)1$ # Tests $5$ points: Basic tests for Combination Generation

$2$

$3$ # Let us start from some base cases.

$4L=[1,2,3,4,5]$

$5$

$6$ # There are no combinations of $5$ elements in groups of $6.$

$7n=0$

$8$ for $c$ in combinations $(6,L)$ :

$9,n+=1$

$10$ check$\_$equal $(n,)$

$11$

$12$

$13$ # There is only one combination of $5$ elements in groups of $5$ : the set itself.

$14n=0$

$15$ for $c$ in combinations $(5,L)$ :

$16$ check$\_$equal $(c,$set$(L))$

$17,n+=1$

$18$ check$\_$equal $(n,1)$

$19$