Giving Away Money

The man can give either $0 ,5,10 ....$ rupees. So the required answer is:

$a_j + a_{2j} +a_{3j}....$ ; where $a_n$ represent coefficient of $x^n$ in the expansion $(1 + x + x^2 +.....+ x^{mj -1}) ^ n$

Plugging in values, we need to find $a_5 + a_{10} +a_{15}$ in $(1 + x + x^2 +.....+ x^{14}) ^ 6$ .

For this we plug in $5^{th}$ roots of unity one by one in the expression and sum it then divide the summation by $5$ . Also it is easy to say that except for $1$ all other $5^{th}$ roots of unity give value $0$ when put into expression so our answer simplifies into:

$\displaystyle \frac{15^{6}}{5} - 1 = \boxed{2278124}$