I was asked a question in an aptitude test, the statement of which is as follows:
"Out of 100 available equally likely choices we have to make 4 random selections. Goal is to have maximum randomness in the selection. Choices can be made in two ways:
You yourself make 4 random selections.
You select 4 random persons put of 100 so that they make 1 random selection out of 100.
Explain the reason behind your answer. Would it make any difference if we change the number of choices of available persons for selection."
This is how I approached toward the problem:
"When I randomly select 4 person out of hundred I would be making 4 choice out of 100 hundred available choice. These 4 choices would be determining my selection of 4 choices that is, event depended choice. In that case it can be possible that two or more persons out of 4 can make same choice thus decreasing randomness.
On the other hand,If I make choices and these choices are random then too repetition can be possible." This is where is am not able to do the reasoning. I seek you help in arriving at some conclusion. Thank you.