Combination Notation

Mrs. Pepmeyer's class won first place in the school's read-a-thon which meant her class could have a sundae party. The class was given $7$ different flavors of ice cream, $4$ flavors of syrups, and $5$ types of toppings. Each student could choose $2$ types of ice cream, $1$ syrup, and $3$ toppings. Assuming each student chooses $2$ flavors of ice cream, $1$ syrup, and $3$ toppings, how many different sundae combinations can a student choose from?