In which position does the subset 2489 occur in the lexicographic order of the 4-subsets of {1,2

step 1 Hey, it's Clarissa with Numerate here. So we're just going to place these in the lexicographic o

In which position does the subset 2489 occur in the...

Key Concepts

Ranking of Subsets

Ranking of subsets in lexicographic order involves determining the exact position or rank of a specific subset among all possible subsets of a certain size, sorted in lexicographic order. This is done by systematically counting all subsets that would appear before the given subset by using combination counts and the rules of lexicographic comparison.

Binomial Coefficients

Binomial coefficients provide the numerical value of the different combinations possible when selecting k elements from a set of n distinct elements. They form the basis for many problems in combinatorics and are crucial for calculating positions or ranks in lexicographic order among subsets, as they allow us to count how many subsets precede a given subset.

Lexicographic Order

Lexicographic order is a method of ordering sequences by comparing the elements in a fixed order, typically from left to right, similar to the way words are ordered in a dictionary. In the context of subsets, this order is determined based on the natural increasing order of the elements in the set, where one subset is considered ‘smaller’ than another if the first element where they differ is smaller in the first set than in the second.

Combination Enumeration

Combination enumeration involves counting the number of ways to choose a subset of items from a larger set when the order of selection does not matter. This is commonly represented by the binomial coefficient, often read as 'n choose k', which is a fundamental concept in combinatorics for determining the total number of possible combinations without regard to order.

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