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}')

# Enter your code here. Read input from STDIN. Print output to STDOUT
import fractions
from itertools import combinations
from itertools import product


Bag1 = ['r']*4 + ['b']*5
Bag2 = ['r']*3 + ['b']*7

Bag2_comb = list(combinations(Bag2,2))

matched = 0
total = len(Bag1) * len(list(combinations(Bag2,2)))

for x in list(product(Bag1, Bag2_comb)):
    if [x[0], x[1][0], x[1][1]].count('b')==2 and [x[0], x[1][0], x[1][1]].count('r')==1:
        matched += 1

print(fractions.Fraction(matched, total))

from fractions import Fraction

bag1 = ['r']*4 + ['b']*5
bag2 = ['r']*3 + ['b']*7

combo = []
visited = 0

for i in bag1:
    for e, j in enumerate(bag2):
        for k in bag2[e+1:]:
            temp = [i, j, k]
            if (temp.count('r') == 1) and (temp.count('b') == 2):
                combo.append(temp)
            
            visited += 1
            
print(Fraction(len(combo), visited))