Suppose a$1,$a$2,,$a$9$ are non$-$negative integers. How many solutions are there to the equation

a$1+$a$2++$a$9=61$

a$)...$ with no further restrictions? ANSWER comb$(69,61)$

b$)...$ where each ai$<=7?$

$($Hint: You might like to use the anti$-$dot method here.$)$

c$)...$ where each ai$<=8?$

Hint: You might like to use the anti$-$dot method here.$)$