Question

undergrad students at college belong to one of four groups depending on the year which they are expected to graduate. each student must choose one of 21 different majors. how many students are needed to assure that there are two students expected to graduate in the same year who have the same major?​

Answer 1

answer is 85

maximum possible different major/group=84

so 85th student must be same as one of those 84 student

Answer 2

Answer:

85

Step-by-step explanation:

Probability is branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of event and 1 indicates certainty.  higher the probability of an event, the more likely it is that event will occur. A simple example is tossing of a fair (unbiased) coin. Since coin is fair, two outcomes ("heads" and "tails") are both equally probable; probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, probability of either of  "heads" or "tails" is 1/2 (which can also be written as 0.5 or 50%).

These concepts have been given a axiomatic mathematical formalization in probability theory, which is not used widely in areas of study such as statistics, mathematic, science, finance, gambling, artificial intelligence, machine learning, computer scienceand game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used as to describe the underlying mechanics and regularities of complex systems.

When dealing with experiments that are random and well-defined in purely theoretical setting (like tossing a coin), probabilities can be numerically described by number of desired outcomes, divided by  total number of all  outcomes. For example, tossing a coin twice will yield "head-head", "head-tail", "tail-head", and "tail-tail" outcomes.  probability of getting an outcome of "head-head" is 1 out of 4 outcomes, or, in numerical terms, 1/4, 0.25 or 25%. However, when it comes to practical application, there are two major competing categories of probability interpretations, whose adherents hold different views about fundamental nature of probability.

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