Question

The number of non negative integral solutions for the equations $a+b+c+d+e=16$ and $a+b+c=7$ is

• A. $36$
• B. $185$
• C. $192$
• D. $360$

Answer 1

The correct option is D $360$

Here, $a+b+c+d+e=16$ and $a+b+c=7$
$\therefore d+e=9$
Number of non negative integral solutions of $a+b+c=7$
$={}^{7+3-1}{C}_{3-1}={}^9{C}_2=36$
Number of non negative integral solutions of $d+e=9$
$={}^{9+2-1}{C}_{2-1}={}^{10}{C}_1=10$
$\therefore$ required solution $=36\times 10=360$