a new pizza chain applies constant pricing and asks customers to choose 6 toppings out of 15 options, allowing multiplicity in the topping choice. for instance, a person who wants a pizza with only mushrooms and olives can select 4 mushrooms and 2 olives. a) [20 pts) How many different types of pizza are possible? 1 b) (30 pts) How many different types of pizza are possible if we are heat-sensitive and the selection of jalapeno cannot exceed 3?

(b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, 8108520 many different sorts of pizza are possible.

Given that,

A brand-new pizza restaurant offers 15 topping choices and consistent cost, allowing customers to select any six of them. For instance, a customer can choose 4 mushrooms and 2 olives if they just want mushrooms and olives on their pizza.

We have to find

a) How many distinct pizza varieties are there.

b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, how many different sorts of pizza are possible.

We know that,

(a) we have 6 places to fill form 15 options.

So, each place has 15 choice

Type of pizza possible=15⁶.

(b) No jalapeno used = 14⁶

1 jalapeno used = 14⁵

2 jalapeno used = 14⁴

3 jalapeno used = 14³

Total pizza = 14³+14⁴+14⁵+14⁶

Total pizza = 14³(1+14+14²+14³)

Total pizza = 8108520

Therefore,

(a) 15⁶ many distinct pizza varieties are there.

(b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, 8108520 many different sorts of pizza are possible.

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