# Pizza Overload

**Discrete Mathematics**Level 2

John goes to a pizzeria which offers 15 toppings. Also, for the customers who would like to taste 2 different toppings while buying a single pizza, they have an option of 'half-n-half' where your pizza can have a combination of two different toppings, say pepperoni and Margarita. Half of the pizza will be having a Margherita topping and half will be having Pepperoni. This is a considered to be a separate topping in itself. Margherita , pepperoni and the combo of half margherita and half pepperoni are considered as 3 different toppings. (Note: the 15 toppings available are 'single' toppings. You can choose from those 15 or create a new topping of your choice which would be a combination of 2 toppings on the same pizza, half of pizza having topping A and half having topping B). John buys 6 pizzas. (John can also buy pizza with exact same topping more than once) . Let the total number of possibilities be \(k\).

Find the value of \( \left \lfloor \dfrac k{100} \right \rfloor \).

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