Are all options in "Present only ___ of total choices" presented an ~equal number of times?

When using the choice randomization option "Present only ___ of total choices" with a multiple choice question, will all of the options in the pool of total choices be presented an approximately equal number of times as multiple respondents take the survey? Seemingly the alternative would be that the selection of which options to present is completely random each time a respondent completes a survey, which means that some choices could appear more times than others; if this is the case, does the system store the number of times a choice is presented in a question even if it is not selected (which would allow us to weight the results)? We know the "Evenly Present Elements" option can be used to help ensure equal representation of elements, but this question pertains to options within a specific multiple choice question.
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For context, we are basically doing A/B testing by asking respondents to select the best option in a multiple choice question. There are ~50 options in the total pool, so we can't present respondents with that many choices to consider. As such, we want the system to select four options from the total pool for each respondent. By having many respondents complete the survey, the best choices should emerge; however, this is conditional on all choices being presented an approximately equal number of times.