Question

The number of positive integral solutions of the equation $a+b+c+d+e=30$ is

• A. $25173$
• B. $23517$
• C. $25731$
• D. $23751$

Answer 1

The correct option is D $23751$

Number of positive integral solutions for $x_1+x_2...+x_n=k$ is ${}^{k-1}{C}_{n-1}$

Here $k=30$ and $n=5$

So number of positive integral solutions $={}^{30-1}{C}_{5-1}={}^{29}{C}_4=23751$