The different types of one-topping pizzas that they serve are 196.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
As the size of the pizzas that are available is of 3 different types, therefore, the number of choices for the size of the pizza is 3, which can be written as,
[tex]\text{Choices of Pizza}=^3C_1[/tex]
The number of toppings that are available is 14, therefore, the number of choices for pizza toppings can be written as,
[tex]\text{Choices of Toppings}=^{14}C_1[/tex]
Now, the different types of one-topping pizzas that they serve are,
[tex]= \text{Choices of Pizza} \times \text{Choices of Toppings}\\\\= ^3C_1 \times ^{14}C_1\\\\=3 \times 14\\\\= 196[/tex]
Hence, the different types of one-topping pizzas that they serve are 196.
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