Question

The number of terms in the expansion $(a+b+c+d{)}^{20}$ is

• A. $1671$
• B. $1717$
• C. $1771$
• D. $7171$

Answer 1

Answer: (C)

$1771$

Given ${(a+b+c+d)}^{20}$ we need to find no. of terms.

No. of terms $=$ No. of non-negative solutions of $x_1+x_2+x_3+x_4=20$

No. of solutions $={}^{n+r-1}{C}_{r-1}$

Here, $n=20,r=4$

$\Rightarrow {}^{23}{C}_3=\frac{23\times 22\times 21}{6}$

$=1771.$

Hence, the answer is $1771.$