Question

The number of solutions of $x_1+x_2+x_3=51(x_1,x_2,x_3$ being odd natural numbers) is : -

• A. 300
• B. 325
• C. 330
• D. 350

Answer 1

The correct option is B 325

Consider $x_1=1$
Then we get $x_2+x_3=50$
$x_2=1,3,5,\mathrm{7...25}$
And
$x_3=49,\mathrm{47...25}$
Hence, total number of ways is 13.
The $x_2$ and $x_1$ can be interchanged.

Hence, total 25 ways.
Similarly we put $x_1=3$ we get 24 ways and so on.

Hence the required permutation will be
$=\frac{26\times 25}{2}$
$=325$.