Question

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

• A. 1870
• B. 1875
• C. 1865
• D. 1880

Answer 1

Answer: (B)

Given, $x_1{x}_2{x}_3{x}_4{x}_5$=1050
$\Rightarrow$$x_1{x}_2{x}_3{x}_4{x}_5$= 2 $\times$3 $\times$ 5${}^2$ $\times$ 7
Each of 2, 3 or 7 can take 5 places and 5${}^2$ can be disposed in 15 ways.
Hence, number of positive integral solution
= 5${}^3$ × 15 = 1875