The number of positive integral solutions satisfying the equation x1⋅x2⋅x3⋅x4⋅x5=240 is

We have, x1⋅x2⋅x3⋅x4⋅x5=240 where x1,x2,x3,x4,x5  are natural numbers.Now, by using prime factorization of 240, we can write the given equation as x1x2x3x4x5=24×3×5Now, we can assign 3 and 5 to any of 5 unknowns in 5 x 5ways.We can assign 24 to x1,x2,x3,x4,x5 ina+b+c+d+e=4 ⇒4+5−1C5−1=8C4, ways ∴ Required number of ways =8C4×25=1750