The statement that the coefficient of xⁿ*y⁾ⁿ in the expansion of (x + y)ⁿ equals binomial(k, n) is false. The correct term is binomial(n, k) according to the binomial theorem.
The statement regarding the coefficient in the binomial expansion of (x + y)ⁿ is false. The correct coefficient of xⁿ*y⁾ⁿ would be determined by the binomial theorem which gives the coefficient as binomial(n, k). It's important to note that binomial(k, n) is incorrect as the roles of n and k have been reversed. The binomial theorem states (x + y)ⁿ equals a sum of terms in the form of binomial(n, r)*x⁾¹*y¹, where r ranges from 0 to n. In this case, to find the coefficient of xⁿ*y⁾ⁿ, the proper form would be binomial(n, k) and not the given binomial(k, n).