Question

The number of positive integral solutions of the equation $x_1{x}_2{x}_3{x}_4{x}_5=1050$ is

• A. 1800
• B. 1600
• C. 1400
• D. 1875

Answer 1

The correct option is D 1875

We have,

$x_1{x}_2{x}_3{x}_4{x}_5=1050=2\times 3\times 5^2\times 7$

Now,

$2,3$ and $7$ can be put in any boxes $x_1,x_2,x_3,x_4$ and $x_5$.

Also $5,5$ can be distributed in $5$ boxes in

${}^{2+5-1}{C}_{5-1}{=}^6{C}_4=15$Ways.

So total no. of positive integral solutions $=15\times 5\times 5\times 5$

$=1875$

Option $D$ is correct answer.