consider the set H of all non$-$negative integer solutions to the equation: a$\_1+$a$\_2+$a$\_3+$a$\_4+$a$\_5=30,$ you can think of H as a set of $6$ tuples of non$-$negative integers that add up to $30)$ you wish to pick one of the elements of H at random and the way you decide to do it is the following: Initialize a $6$ tuple to be all zeros $(0,0,0,0,0,0).$ Roll a fair $6$ sided die $30$ times. For each roll that shows a $1,$ increment the $1$st position, for each roll that shows a $2,$ increment the $2$nd position and so on$.($include a justification of each problem.$)($a$)$ What is the probability that you get the element:$(5,5,5,5,5,5)?$