python math - assuming 25 students in the class, then have the same birthday probability is how much?

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The same class have the same birthday probability.

A class has 25 students, the number of birthdays in the same day, the probability is that?
Code:

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import numpy as np 
from numpy import random
NUM_STUDENT = 25
NUM_EXER = 10000
count=0
for i in range(NUM_EXER):
 birtdays = []
 for j in range(NUM_STUDENT):
 birtdays.append(np.random.randint(356))
 if len(set(birtdays)) < NUM_STUDENT:
 count +=1
print(count/NUM_EXER)

Repeat 10,000 times test python, the probability of 57.6%. As long as there are 25 students, there is a possibility that more than half of likely birthdays on the same day.

Direct calculation:

Probability does not appear the same birthday:
Here Insert Picture Description
probability is the same birthday occurs: 1-p 1-p1- p

When n = 25, is calculated using the python:

def factorial(n):
 a = 1
 for i in range(1, n+1):
 a = a*i
 return a
k = 1 - factorial(365)/(factorial(365-NUM_STUDENT)*365**NUM_STUDENT)
print(k)

Output 56.8%

Several tests have some errors, perhaps python calculation rounding? Or what went wrong?

postscript

Why is there such a situation?
Here Insert Picture Description