13 Probability using combinations

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import itertools
import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats, special

khanacademy

flips = np.arange(1, 9, 1)
total_outcomes = 2 ** 8

c = list(itertools.combinations(flips, 3))

c

[(1, 2, 3),
 (1, 2, 4),
 (1, 2, 5),
 (1, 2, 6),
 (1, 2, 7),
 (1, 2, 8),
 (1, 3, 4),
 (1, 3, 5),
 (1, 3, 6),
 (1, 3, 7),
 (1, 3, 8),
 (1, 4, 5),
 (1, 4, 6),
 (1, 4, 7),
 (1, 4, 8),
 (1, 5, 6),
 (1, 5, 7),
 (1, 5, 8),
 (1, 6, 7),
 (1, 6, 8),
 (1, 7, 8),
 (2, 3, 4),
 (2, 3, 5),
 (2, 3, 6),
 (2, 3, 7),
 (2, 3, 8),
 (2, 4, 5),
 (2, 4, 6),
 (2, 4, 7),
 (2, 4, 8),
 (2, 5, 6),
 (2, 5, 7),
 (2, 5, 8),
 (2, 6, 7),
 (2, 6, 8),
 (2, 7, 8),
 (3, 4, 5),
 (3, 4, 6),
 (3, 4, 7),
 (3, 4, 8),
 (3, 5, 6),
 (3, 5, 7),
 (3, 5, 8),
 (3, 6, 7),
 (3, 6, 8),
 (3, 7, 8),
 (4, 5, 6),
 (4, 5, 7),
 (4, 5, 8),
 (4, 6, 7),
 (4, 6, 8),
 (4, 7, 8),
 (5, 6, 7),
 (5, 6, 8),
 (5, 7, 8),
 (6, 7, 8)]

len(c) / total_outcomes

0.21875

special.comb(len(flips), 3) / total_outcomes

0.21875