Counting

Suppose the friends are A, B, C, Dhruv (D), E. Then denote the number of chocolate gotten by each person as $x_A, x_B, \cdots, x_E$.

The problem becomes to count the nonnegative integer solutions of $x_A+x_B+x_C+x_D+x_E=8$ with $x_D \geq 6$.

We make the substitution $y_A=x_A, y_B=x_B, y_C=x_C, y_D=x_D-6,y_E=x_E$. Then the equation becomes $y_A+y_B+y_C+y_D+y_E=2$. We will count the nonnegative integer solutions of this equation to get the answer. The answer is $\displaystyle \binom{2 + 5 - 1}{5 - 1} = 15$.