Combinatorial identity

by | Oct 28, 2021 | Homework Help

Consider the following combinatorial identity: H HE: _ n—lk=1 (:1) Present a combinatorial argument for this identity by considering a set of :1 people and determining, in two ways,the number of possible selections of a committee of any size and a chairperson for the committee.Hint: (i) How many possible selections are there of a commit-tee of size k and its chairperson? (ii) How many possible selections are there of a chair-person and the other conunittee members? (b) Verify the following identity for n, = 1, 2, 3, 4, S: Z(:)k2=2”_2n(n + 1) k=1 For a combinatorial proof of the preceding, consider a setof :1 people and argue that both sides of the identity rep- resent the number of different selections of a committee,its chairperson, and its secretary (possibly the same as the chairperson).Hint: (i) How many different selections result in the commit-tee containing exactly k people? (ii) How many different selections are there in whichthe chairperson and the secretary are the same?(ANSWER: n2”‘1 .) (iii) How many different selections result in the chairper-son and the secretary being different? (c) Now argue that

Plagiarism-free and delivered on time!

We are passionate about delivering quality essays.

Our writers know how to write on any topic and subject area while meeting all of your specific requirements.

Unlike most other services, we will do a free revision if you need us to make corrections even after delivery.