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  • A pizza place offers 3 different sauces and 4 different toppings. If a customer can choose any combination of one sauce and two toppings (including no toppings), how many different pizza combinatio

A pizza place offers 3 different sauces and 4 different toppings. If a customer can choose any combination of one sauce and two toppings (including no toppings), how many different pizza combinations are possible?

Option: 1

22


Option: 2

33


Option: 3

13


Option: 4

53


Answers (1)

best_answer

To calculate the number of different pizza combinations, we need to consider the options for the sauce and toppings.

For the sauce, there are 3 options to choose from.

For the toppings, since the customer can choose any combination of two toppings, including no toppings, we need to consider the possibilities:

Case 1: No toppings: There is only one option, which is to have no toppings.

Case 2: 1 topping: There are 4 options to choose from for the single topping.

Case 3: 2 toppings: To calculate the number of combinations for 2 toppings, we can use the combination formula: \mathrm{C(4,2)=4 ! /(2 ! \times(4-2) !)=6}.

To find the total number of different pizza combinations, we multiply the number of options for the sauce with the sum of possibilities for the toppings:

\begin{aligned}& \mathrm{3 (sauce ~options) \times(1 (no~ toppings) +4(1 ~topping) +6(2 toppings ))}= \\ &3 \times(1+4+6)=3 \times 11=33. \end{aligned}

Therefore, there are 33 different pizza combinations possible.

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seema garhwal

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