A person has a set of coins consisting of half dollars (50¢), quarters (25¢), dimes (10¢), and nickels (5¢) (indicated coins only). If the person aims to have total 50¢, find all combinations of the number of coins of each denomination the person should take (in order to get exactly 50¢). Note: Organize a presentation of the problem's solution in a table. (Be advice, that a case of zero coins of any denomination is possible.) Extra: Proof that all combinations are found.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.