The number of positive integral solution  of the equation  x1x2x3x4x5=1050 is

Using prime factorization of 1050, we can write the given equation asx1x2x3x4x5=2×3×52×7We can assign 2, 3 or 7 to any of 5 variables. We can assign entire 52 to just one variable in 5 ways or can assign 52= 5 × 5 to two variables in  5C2 ways. Thus,52 can be assigned in 5C1+5C2=5+10=15 waysThus, the required number of solutions is 5 × 5 × 5 × 15 = 1875.