import numpy.random

# We can also import code from scipy to calculate binomial coefficients and
# factorials. NOTE: you don't need this for the birthday simulation code in Task
# 2.1, I just mention it here because you can use it to calculate the numerical
# values for the questions in section 1.
from scipy.special import binom, factorial

# binom(n, k) computes "n choose k":
print(binom(3, 1))
print(binom(4, 2))

# factorial(n) computes n!
print("5! =", factorial(5))
print("10! =", factorial(10))

# numpy.random.randint(low, high) returns a random integer n such that low <= n < high
print(numpy.random.randint(1, 100))
print(numpy.random.randint(1, 3))

# We can generate many at once by passing a third size parameter. It will
# then return an array with that many random numbers. 
mynums = numpy.random.randint(1, 100, size=5)
print(mynums)
print("mynums has %d elements" % len(mynums))
print(mynums[2])

morenums = numpy.random.randint(1, 2, size=5)
# Notice they must all be =1, since each returned n will satisfy 1 <= n < 2
print(morenums)

### WARNING WARNING WARNING ###

# There is also a random.randint(low, high) function in the default python
# library which returns random integers such that low <= n <= high. (whereas
# numpy's version requires < high instead). So, be mindful of which version you
# are using and the differences!

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