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  • A pizza place offers 5 different toppings, and a customer must choose at least 1 topping, but no more than 4 toppings, for their pizza. How many different pizza combinations are possible? n

A pizza place offers 5 different toppings, and a customer must choose at least 1 topping, but no more than 4 toppings, for their pizza. How many different pizza combinations are possible?
 

Option: 1

50


Option: 2

10


Option: 3

20


Option: 4

30


Answers (1)

best_answer

To calculate the number of different pizza combinations, we need to consider the options for the number of toppings the customer can choose: 1,2,3, or 4 toppings.

Case 1: 1 topping:
There are 5 options to choose from for the single topping.

Case 2: 2 toppings:
To calculate the number of combinations for 2 toppings, we can use the combination formiula: \mathrm{C(5,2)=5 ! /(2 ! \times(5-2) !)=10.}

Case 3: 3 toppings:
Similarly, using the combination formula: \mathrm{C(5,3)=5 ! /(3 ! \times(5-3) !)=10.}

Case 4: 4 toppings:
Using the combination formula: \mathrm{C(5,4)=5 ! /(4 ! \times(5-4) !)=5.}

To find the total number of different pizza combinations, we sum the possibilities from all the cases: \mathrm{5 ( 1 ~topping )+10 ( 2 ~toppings )+10 ( 3 ~toppings )+5 ( 4 ~toppings )=30.}

Therefore, there are 30 different pizza combinations possible.

Posted by

Divya Prakash Singh

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