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  4. The number of positive integral solutions of the equation x1 x2x3x4x5=1050 is

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Q. The number of positive integral solutions of the equation $x_1 x_2x_3x_4x_5$=1050 is

VITEEEVITEEE 2007

Solution:

Given, $x_1 x_2x_3x_4x_5$=1050
$\Rightarrow $$x_1 x_2x_3x_4x_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