Part 1) Completely Randomized Experiment
Place all of the names in a hat, and randomly select each person. You can use computer software to do this much more efficiently. Assign each person a number, and then have the computer generate a random number. Any repeats are ignored. Using either method (the hat or computer software) will generate a simple random sample (SRS). Apply this technique to fill out the three groups (those who take the 100 mg pill, those who take the 50 mg, and those who get the placebo)
Since there are 60 people overall, it probably makes the most sense to have each group mentioned have 60/3 = 20 people. Though there isn't a hard fast rule that says each group needs to be equal.
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Part 2) Randomized Block Design
The simple random sampling (SRS) method in part 1 will eliminate as much bias as possible; however, there's a problem in that we might make the groups imbalanced in terms of gender. Consider a scenario where all 20 women go into one group. That group would be 100% overrepresented in terms of capturing the female demographic of the study, while at the same time the men are 100% underrepresented for this particular group.
How can we fix such a possible scenario? By introducing blocks. We'll have the "male" block and the "female" block.
Within the male block, we randomly pick from just the males to fill out the three groups (100 mg, 50 mg, placebo). The female block is handled the same exact way, but this time the researchers select only the women. Since neither 40 nor 20 are multiples of 3, this means that it's impossible to evenly divide the participants among the three groups. Fortunately, it won't drastically affect the results too much.
Side note: you can replace the variable "gender" with any other aspect you prefer (such as age perhaps).
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Summary:
A simple random sample (SRS) will randomly assign people to either the 100 mg, 50 mg or placebo group. There's no guarantee that we'll have an even balance in terms of gender. A randomized block design will guarantee better balance and representation of gender, while still retaining the random nature.
