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

Solution:

Using prime factorization of 1050, we can write the given equation as

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

We can assign 2, 3 or 7 to any of 5 variables. We can assign entire $5^2$ to just one variable in 5 ways or can assign $5^2$= 5 × 5 to two variables in ${ }^5{C}_2$ ways. Thus,$5^2$ can be assigned in

${ }^5{C}_1{+}^5{C}_2=5+10=15$ ways

Thus, the required number of solutions is 5 × 5 × 5 × 15 = 1875.