# For a block randomized experiment how many possible unique assignments are there?

In a block randomized experiment say of 4 individuals split into 2 even blocks with 1 individual in each block getting assigned to treatment and the other control, how many possible unique assignments are there?

My initial thought is that first there are $${4 \choose 2 }*\frac{1}{2}$$ ways to assign the 4 individuals into the 2 blocks.

Then for each block there are $${2 \choose 1}$$ ways to assign which individual gets the treatment and which does not. Then combining the 2 blocks, there are $${4 \choose 2 }*\frac{1}{2} * {2 \choose 1} * {2 \choose 1} = 24$$ unique assignments possible.

Is this correct?