At a made$-$to$-$order sandwich restaurant, there are $3$ choices of bread $($white$,$ wheat or rye$),5$ choices of meat $($chicken$,$ pork, beef, ham, or fish$),$ and $10$ choices of vegetables. Suppose a customer can pick only one kind of bread, only one kind of meat or no meat at all, and at least $1$ vegetable up to as many as he$/$she wants.

$($a$)$ If you ask the server to surprise you with a sandwich, what is the chance that it is wheat or white, with at least $2$ out of $6$ vegetables that you like, and no fish.

$n(s)=C_1^3(C_{1or}^5+C_{i_{no\text{m}\text{e}\text{a}\text{t}}^5}^5)(C_1^{10}+C_2^{10}+C_3^{10}+C_4^{10}+C_5^{10}+C_6^{10}+C_7^{10}+C_8^{10}+C_9^{10}+C_{10}^{10})$

$($b$)$ If your friend picks a sandwich with $5$ kinds of vegetables, what is the chance that it is ham or beef on rye with tomatoes and lettuce.

$($c$)$ If your friend picks a sandwich with at least $5$ that is the chance that is ham on rye with tomatoes or lettuce.