Find the 4th term in the binomial expansion. $( x + y ) ^ { n }$
A) $\frac { ( n - 3 ) ! } { ( n - 3 ) ! 3 ! } x ^ { n - 3 } y ^ { 3 }$
B) $\frac { n ! } { ( n - 4 ) ! 4 ! } x ^ { n - 4 } y ^ { 4 }$
C) $\frac { n ! } { ( n - 3 ) ! 3 ! } x ^ { n - 3 } y ^ { 3 }$
D) $\frac { n ! } { ( n - 4 ) ! } x ^ { n - 4 } y ^ { 4 }$
E) $\frac { n ! } { ( n - 3 ) ! 3 ! } x ^ { n - 3 } y ^ { n }$

Question

Quizplus · Accepted Answer

The fourth term in the binomial expansion is determined by the combination $\binom {n}{3}$ and the powers of x and y in the term are $x^{n-3}y^3$. Simplifying the expression for this combination, we get $\frac{n!}{(n-3)!3!}$. Thus the correct option is C.

Find the 4th Term in the Binomial Expansion (x+y)n( x + y ) ^ { n }(x+y)n

Find the 4th Term in the Binomial Expansion $( x + y ) ^ { n }$