You should add a few sentences to explain your reasoning. And the question is "what are", not "how many", so can you say something more about them?.agargento said:I think the answer is 2n/2 ... to include just even numbers. Is my reasoning correct?
FactChecker said:You should add a few sentences to explain your reasoning. And the question is "what are", not "how many", so can you say something more about them?.
That is better. It never hurts to add a brief explanation like that.agargento said:Just bad translation on my part. "How many" is more correct. As for reasoning, we were taught in class that for n objects, you have 2n possibilities for subsets. So I thought that because we have n/2 objects (we want only even numbers) 2n/2 is the answer.
FactChecker said:That is better. It never hurts to add a brief explanation like that.
It is correct. The odd numbers are irrelevant.agargento said:But is it correct?
PeroK said:It is correct. The odd numbers are irrelevant.
Oh now I got it. Thanks!PeroK said:That's the empty set. That is included as one of the ##2^n## subsets. If you are looking for non-empty subsets then there are only ##2^n -1## of those.
In this case you were explicitly told to count the empty set.
Combinations and permutations are both ways to arrange a set of objects, but they differ in the order in which the objects are arranged. Combinations do not take into account the order, while permutations do. For example, the combinations of ABC are ABC, ACB, BAC, BCA, CAB, CBA, while the permutations are ABC, ACB, BAC, BCA, CAB, CBA.
The formula for calculating combinations is nCr = n! / r!(n-r)!, where n is the total number of objects and r is the number of objects being selected. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being selected.
The principle of inclusion-exclusion is a counting technique used to calculate the size of a set that is the union of multiple smaller sets. It states that the size of the union of two sets is equal to the sum of their sizes minus the size of their intersection.
Combinatorics can be used to solve problems in a variety of fields, such as genetics, computer science, and economics. For example, it can be used to calculate the number of possible outcomes in a genetics cross, the number of possible outcomes in a computer password, or the number of possible combinations of items in a store.
A set is a collection of distinct objects, while a subset is a set that contains only some of the objects from a larger set. In other words, a subset is a smaller set within a larger set. For example, the set {1, 2, 3} is a subset of the set {1, 2, 3, 4}.