Writing coefficient of a term

Question

Assignment:

(a) Use the Binomial Theorem to write the expansion of (x + y)⁶?
(b) Write the coefficient of the term x²y⁴z⁵  expansion of (x + y + z)¹¹. 

Let A = {a, b, c, d}, and let R be the relation defined on A by the following matrix:

(a) Describe R by listing the ordered pairs in R and draw the digraph of this relation.

(b) Which of the properties: reflexive, antisymmetric and transitive are true for the given relation?  Begin your discussion by defining each term in general first and then how the definition relates to this specific example.
(c) Is this relation a partial order? Explain.  If this relation is a partial order, draw its Hasse diagram.

Provide complete and step by step solution for the question and show calculations and use formulas.