Find the 5th term in the binomial expansion. $( a - b ) ^ { n }$
A) $\frac { n ! } { ( n - 5 ) ! 5 ! } a ^ { n - 5 } b ^ { 5 }$
B) $\quad \frac { ( n - 4 ) ! } { ( n - 4 ) ! 4 ! } a ^ { n - 4 } b ^ { 4 }$
C) $\frac { n ! } { ( n - 4 ) ! 4 ! } a ^ { n - 4 } b ^ { 4 }$
D) $\frac { n ! } { ( n - 4 ) ! } a ^ { n - 4 } b ^ { 4 }$
E) $\frac { n ! } { ( n - 5 ) ! 5 ! } a ^ { n - 5 } b ^ { n }$

Question

Quizplus · Accepted Answer

The 5th term in the binomial expansion is given by the coefficient of $a^{n-4}b^4$, which is $\binom{n}{4}=\frac{n!}{(n-4)!4!}$. Therefore, the answer is choice C.

Find the 5th Term in the Binomial Expansion (a−b)n( a - b ) ^ { n }(a−b)n

Find the 5th Term in the Binomial Expansion $( a - b ) ^ { n }$