09 Intro to 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

persons = ['A', 'B', 'C', 'D', 'E', 'F']
seats = [1, 2, 3]

p = list(itertools.permutations(persons, len(seats)))

p

[('A', 'B', 'C'),
 ('A', 'B', 'D'),
 ('A', 'B', 'E'),
 ('A', 'B', 'F'),
 ('A', 'C', 'B'),
 ('A', 'C', 'D'),
 ('A', 'C', 'E'),
 ('A', 'C', 'F'),
 ('A', 'D', 'B'),
 ('A', 'D', 'C'),
 ('A', 'D', 'E'),
 ('A', 'D', 'F'),
 ('A', 'E', 'B'),
 ('A', 'E', 'C'),
 ('A', 'E', 'D'),
 ('A', 'E', 'F'),
 ('A', 'F', 'B'),
 ('A', 'F', 'C'),
 ('A', 'F', 'D'),
 ('A', 'F', 'E'),
 ('B', 'A', 'C'),
 ('B', 'A', 'D'),
 ('B', 'A', 'E'),
 ('B', 'A', 'F'),
 ('B', 'C', 'A'),
 ('B', 'C', 'D'),
 ('B', 'C', 'E'),
 ('B', 'C', 'F'),
 ('B', 'D', 'A'),
 ('B', 'D', 'C'),
 ('B', 'D', 'E'),
 ('B', 'D', 'F'),
 ('B', 'E', 'A'),
 ('B', 'E', 'C'),
 ('B', 'E', 'D'),
 ('B', 'E', 'F'),
 ('B', 'F', 'A'),
 ('B', 'F', 'C'),
 ('B', 'F', 'D'),
 ('B', 'F', 'E'),
 ('C', 'A', 'B'),
 ('C', 'A', 'D'),
 ('C', 'A', 'E'),
 ('C', 'A', 'F'),
 ('C', 'B', 'A'),
 ('C', 'B', 'D'),
 ('C', 'B', 'E'),
 ('C', 'B', 'F'),
 ('C', 'D', 'A'),
 ('C', 'D', 'B'),
 ('C', 'D', 'E'),
 ('C', 'D', 'F'),
 ('C', 'E', 'A'),
 ('C', 'E', 'B'),
 ('C', 'E', 'D'),
 ('C', 'E', 'F'),
 ('C', 'F', 'A'),
 ('C', 'F', 'B'),
 ('C', 'F', 'D'),
 ('C', 'F', 'E'),
 ('D', 'A', 'B'),
 ('D', 'A', 'C'),
 ('D', 'A', 'E'),
 ('D', 'A', 'F'),
 ('D', 'B', 'A'),
 ('D', 'B', 'C'),
 ('D', 'B', 'E'),
 ('D', 'B', 'F'),
 ('D', 'C', 'A'),
 ('D', 'C', 'B'),
 ('D', 'C', 'E'),
 ('D', 'C', 'F'),
 ('D', 'E', 'A'),
 ('D', 'E', 'B'),
 ('D', 'E', 'C'),
 ('D', 'E', 'F'),
 ('D', 'F', 'A'),
 ('D', 'F', 'B'),
 ('D', 'F', 'C'),
 ('D', 'F', 'E'),
 ('E', 'A', 'B'),
 ('E', 'A', 'C'),
 ('E', 'A', 'D'),
 ('E', 'A', 'F'),
 ('E', 'B', 'A'),
 ('E', 'B', 'C'),
 ('E', 'B', 'D'),
 ('E', 'B', 'F'),
 ('E', 'C', 'A'),
 ('E', 'C', 'B'),
 ('E', 'C', 'D'),
 ('E', 'C', 'F'),
 ('E', 'D', 'A'),
 ('E', 'D', 'B'),
 ('E', 'D', 'C'),
 ('E', 'D', 'F'),
 ('E', 'F', 'A'),
 ('E', 'F', 'B'),
 ('E', 'F', 'C'),
 ('E', 'F', 'D'),
 ('F', 'A', 'B'),
 ('F', 'A', 'C'),
 ('F', 'A', 'D'),
 ('F', 'A', 'E'),
 ('F', 'B', 'A'),
 ('F', 'B', 'C'),
 ('F', 'B', 'D'),
 ('F', 'B', 'E'),
 ('F', 'C', 'A'),
 ('F', 'C', 'B'),
 ('F', 'C', 'D'),
 ('F', 'C', 'E'),
 ('F', 'D', 'A'),
 ('F', 'D', 'B'),
 ('F', 'D', 'C'),
 ('F', 'D', 'E'),
 ('F', 'E', 'A'),
 ('F', 'E', 'B'),
 ('F', 'E', 'C'),
 ('F', 'E', 'D')]

len(p)

120

c = list(itertools.combinations(persons, len(seats)))

c

[('A', 'B', 'C'),
 ('A', 'B', 'D'),
 ('A', 'B', 'E'),
 ('A', 'B', 'F'),
 ('A', 'C', 'D'),
 ('A', 'C', 'E'),
 ('A', 'C', 'F'),
 ('A', 'D', 'E'),
 ('A', 'D', 'F'),
 ('A', 'E', 'F'),
 ('B', 'C', 'D'),
 ('B', 'C', 'E'),
 ('B', 'C', 'F'),
 ('B', 'D', 'E'),
 ('B', 'D', 'F'),
 ('B', 'E', 'F'),
 ('C', 'D', 'E'),
 ('C', 'D', 'F'),
 ('C', 'E', 'F'),
 ('D', 'E', 'F')]

len(c)

20

special.perm(6, 3) 

120.0

special.perm(6, 3) / np.math.factorial(3)

20.0

special.comb(6, 3)

20.0