As the statistician on a multidisciplinary research team, you are asked to create a randomization scheme to assign three treatments A, B, and $\mathrm{C}$, to 150 units in blocks of 6 . The scheme must ensure that each treatment is assigned to 50 units and that a block is randomly selected when a unit is randomized.

a. How many permuted blocks are required?

b. Use $\mathrm{R}$ to create a randomization scheme that satisfies the requirements. The program should return a data frame where each row represents a unit with three columns representing the assigned block, the assigned treatment, and the unit number from 1 to 150.