A researcher wishes to design a fully blocked experiment wit

A researcher wishes to design a fully blocked experiment with groups of subjects representing every possible combination of 1 explanatory variable (control versus treatment) and 4 other variables (male versus female, old versus young, healthy versus ill, and normal weight versus overweight) for a total of 5 variables.

Solution

let us lokk of this like those binary numbers with the 1 and 0.
Zero represents the option on the left, One represents the option on the right
For example control is on the left it is zero, female is on the right so one.
000000 means control,male,old,healthy,black,normalwei...
000001 means control,male,old,healthy,black,over-weig...
010001 means control,female,old,healthy,black,over-we...
.
.

The answer is 2^5 that is 32. That means 2 to the 5th power
In an easier way to think of this is, you have 5 variables, but each variable can be one of two things. This is a classic use for 2^x. In this case x = 5 and that means 2^5 = 32

Option D is the final answer