from math import gcd

def prob(red_1, black_1, red_2, black_2):
    
    # Total outcomes
    total_1 = red_1 + black_1
    total_2 = red_2 + black_2
  
    total_outcomes = total_1 * (total_2 * (total_2 - 1) // 2)
    
    # Favorable outcomes
    # Black from Bag 1, 1 red + 1 black from Bag 2
    BRB = black_1 * (red_2 * black_2)   
    
    # Red from Bag 1, 2 blacks from Bag 2
    RBB = red_1 * (black_2 * (black_2 - 1) // 2)
    
    favorables = BRB + RBB
    
    divisor = gcd(favorables, total_outcomes)
    num = favorables // divisor
    den = total_outcomes // divisor
    
    return f"{num}/{den}"

from fractions import Fraction 
from itertools import combinations

bag_1=['r','r','r','r','b','b','b','b','b']
bag_2=['r','r','r','b','b','b','b','b','b','b']
all_pairs=[]
num=0
for item1_bag_1 in (bag_1):
  for item2_bag_2,item3_bag2 in (combinations(bag_2,2)):
    all_pairs.append((item1_bag_1,item2_bag_2,item3_bag2))
for bbr in all_pairs:
  if bbr.count('r')==1 and bbr.count('b')==2:
    num+=1
print(Fraction(num,len(all_pairs)))

import math

# setup situation
bag1 = ['r']*4 + ['b']*5    # 1 pick
bag2 = ['r']*3 + ['b']*7    # 2 picks
                            # b b r

# initialize counting variables
numerator = 0
denominator = 0

# collect event occurrences
for X in bag1:  # 1 pick from bag1
    
    for Y1 in bag2:  # 1 pick from bag2
        bag2reduced = bag2.copy()  # create a COPY of bag2
        bag2reduced.remove(Y1)  # remove already picked element from COPY of bag2
        
        for Y2 in bag2reduced:  # 1 pick from EDITED bag2
            tup = (X, Y1, Y2)  # event
            
            if all([tup.count('r') == 1,
                    tup.count('b') == 2]):  # conditions of interest
                numerator += 1
            
            denominator += 1

gcd = math.gcd(numerator, denominator)

numerator //= gcd
denominator //= gcd

print(f'{numerator}/{denominator}')