Question

The number of terms in the expansion of $(a+b+c+d+e{)}^3$ is

• A. $20$
• B. $24$
• C. $27$
• D. $35$

Answer 1

The correct option is D $35$

The no. of terms in $(a+b+c+d+e)$ are $5$ and exponent, $n=3$
Therefore, total number of terms in the expansion of $(a+b+c+d+e{)}^3$ are
${}^{n+r-1}{C}_n$
Now, $r=5$ and $n=3$
${}^{3+5-1}{C}_3$ $={}^7{C}_3$

$=\frac{7\cdot 6\cdot 5}{3!}$ $=35$