# for factorial and combinations
import math 
# for rolling dice
import random
# for a convenient average function
import numpy as np

# generate a random integer in [1, 6]
die = random.randint(1, 6)
print(die)
# reroll the die if we want to
die = random.randint(1, 6)
print(die)

# generate a list of rolls
rolls = [random.randint(1, 6) for i in range(5)]
print(rolls)
# re roll them if we want
rolls = [random.randint(1, 6) for i in range(5)]
print(rolls)


print(np.average(rolls))
rolls = [random.randint(1, 6) for i in range(5)]
print(np.average(rolls))
rolls = [random.randint(1, 6) for i in range(1000)]
print(np.average(rolls))
rolls = [random.randint(1, 6) for i in range(10000)]
print(np.average(rolls))
rolls = [random.randint(1, 6) for i in range(100000)]
print(np.average(rolls))

# some examples with factorial
print(math.factorial(10))
print(math.factorial(5))
# n choose k
print(math.comb(10, 6))

# what are the chances of turtle being happy for
# *exactly* 6 of the next 10 days?
print(math.comb(10, 6) * (0.85 ** 6) * ((1 - 0.85) ** 4))