IN PYTHON:

Write a function possible$\_$study$\_$groups$($zbinis$).$ The parameter zbinis is a list of Zoomerbinis of the same form as in Task $2.$

The function should return a list representing all the possible ways a valid study group could be chosen from zbinis. Each element is a tuple where:

The first element is a tuple of indices representing a group. This tuple should contain exactly three or four unique indices into the zbinis list in ascending order.

The second element is a score for the group, derived using a "points" system $($described below$).$

For example, if zbinis was of length four, there could be up to five tuples of indices in the result with the first element in each being: $(0,1,2,3),(0,1,2),(0,1,3),(0,2,3)$ and $(1,2,3)$

Each group's score $($the second element in each returned tuple$)$ is derived using a "points" system according to the following rules:

Add three points for each subject shared by all members of the group, and;

Add one point if the group has three members, or two points if the group has four members.

The returned groups should be sorted in descending order using the above scoring system, that is$,$ higher scored groups should come before lower scored groups in the resulting list.

If there is ever a tie in scores, the group's indices should be used as a tiebreaker. Each index should be considered in turn $($left to right$)$ until one facilitates a tiebreak. For example, the grouping $(0,2,3)$ should come before $(1,2,3),$ and $(0,1,2)$ should come before $(0,1,3).$

Groups that are invalid as per the same rules as in Task $2$ should be excluded from the returned list altogether. A working version of the respective valid$\_$study$\_$group$($zbinis$,$ group$)$ function has been provided to help you with this task.

Example Calls:

$>>>$ print$($possible$\_$study$\_$groups$([(198,[\text{'}$FoC$\text{'}]),(138,[\text{'}$FoC$\text{'},$ 'Calc $1\text{'}]),(14,[\text{'}$FoC$\text{'},$ 'Calc $1\text{'}]),(66,[\text{'}$Calc $1\text{'}])]))$

$[((0,1,2),4),((1,2,3),4)]$

$>>>$ print$($possible$\_$study$\_$groups$([(198,[\text{'}$FoC$\text{'}]),(138,[\text{'}$FoC$\text{'},$ 'Calc $1\text{'}]),(14,[\text{'}$FoC$\text{'}]),(66,[\text{'}$FoC$\text{'}])]))$

$[((0,1,2,3),5),((0,1,2),4),((0,1,3),4),((0,2,3),4),((1,2,3),4)]$

$>>>$ print$($possible$\_$study$\_$groups$([(198,[\text{'}$FoC$\text{'}]),(138,[\text{'}$Calc $1\text{'}]),(14,[\text{'}$Calc $1\text{'}]),(66,[\text{'}$FoC$\text{'}])]))$

$[]$