Evenly distributed random strings in Python

I want to generate random strings (or arrays) of 1's and 0's. Then I classify them according to quantity (count) of 1's. I want the generated strings to be evenly distributed among the possible counts.

But the following code gives me a normal distribution:

import numpy as np

for i in range(num_examples):
    seq = np.random.randint(2, size=(seq_length)).astype('float32')
    sequences[i] = seq

target_classes = []
for input in sequences: 
    target = (input == 1).sum()
    target_classes.append(target)

The histogram of counts is:

A NumPy solution would be awesome. Or do I need regular expressions or something else?