Equal chance of random selection when halves of set are balanced?

Design: For 18 trials numbers (either 0 or 1) are randomly selected, a random portion of the first 9 are 0 and the last 9 are set as the opposite number of 0s. Within the first and last 9 the 0 or 1s are randomly assorted. The numbers are described as being in 3 consecutive groups of 6 called ‘blocks’.

Question: in the above approach the middle block contains half trials with the first 9 percentage of 0s and last 9 the other percentage of 0s. Because the 0 and 1s are randomly assorted does the middle block have an equal chance of containing all or no 0s as the other blocks?