At a particular company, security codes must be ten digit numbers.Three of the digits must come from $\{1,4,5,7\},$ three of the digits must come from $\{2,3,6\},$ and four of the digits must come from $\{0,8,9\}.$ Repetition of digits is allowed.$($a$)$ How many security codes are there?$($b$)$ How many of these security codes neither start with $1$ nor end with $9?$ HINT: To choose positions for the numbers of the different sets $($i$.$e$.\{1,4,5,7),\{2,3,6\}$ &$\{0,8,9\})$ use the multinomial coefficient.