$6.(15$ points$)($a$)$ How many binary strings of length $6$ are there?$($b$)$ How many binary strings of length $6$ have exactly three $0$s$?($c$)$ How many strings of length $6$ from the alphabet $0,1,2$ are there?$($d$)$ How many strings of length $6$ from the alphabet $0,1,2$ have exactly three $0$s$?($e$)$ How many strings of length $6$ from the alphabet $0,1,2$ have less than three $0$s$?$