combination_problem.py

from itertools import combinations
number_of_items = 8
number_of_draws = 6
iter_sets = combinations([i for i in range(number_of_items)], number_of_draws)
sets = list(iter_sets)

for s in sets:
  print(s)

len(sets)


for s in sets:
  cond = (0 in s) and (1 in s) and (2 in s) and (3 in s)
  if cond:
    print(s)

"""
(n choose d)
given n=8 distinct elements, draw all sets of d=6 elements. 

QUESTION: how many of those sets have [0, 1, 2, 3]=[0...r=4 exclusive]

We can call subsetR=[0...r]

since r items of each set of d is fixed:
(since 4 items of each set of 6 is fixed)

6-element-set = subsetR + subsetV
1. v = d - r = 2 = number of items in the set that is not fixed (subsetV)
2. p = n - r = 4 = number of items that you can select for subsetV


(p choose v)
ANSWER: given p=4 distinct elements, draw all sets of v=2


total number of combinations when you pick 10 of 100
100!
----
90!10!

total number of combinations of 10 that has (1, 2, 3, 4, 5)
v = 10 - 5 = 5
p = 100 - 5 = 95
95!
------
90!5!


probability

   95!
  ----
  90!5!
----------
  100!
  ----
  90!10!

"""