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  • A pizza place offers 6 different toppings, but a customer can choose at most 4 toppings for their pizza. How many different pizza combinations are possible?  <div class='qna-option'

A pizza place offers 6 different toppings, but a customer can choose at most 4 toppings for their pizza. How many different pizza combinations are possible?
 

Option: 1

65


Option: 2

53


Option: 3

57


Option: 4

63


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: 0,1,2,3, or 4 toppings.
Case 1: 0 toppings:
In this case, there is only one option, which is to have no toppings.

Case 2: 1 topping:
There are 6 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(6,2)=6 ! /(2 ! \times(6-2) !)=15.}

Case 4: 3 toppings:
Similarly, using the combination formula: \mathrm{C(6,3)=6 ! /(3 ! \times(6-3) !)=20.}

Case 5: 4 toppings:
Using the combination formula: \mathrm{C(6.4)=6 ! /(4 ! \times(6-4) !)=15.}

To find the total number of different pizza combinations, we sum the possibilities from all the cases: \mathrm{1 (0 ~toppings )+6 ( 1 ~topping )+15 ( 2 ~toppings )+20 (3 ~toppings )+15 (4 ~toppings )=57.}

Therefore, there are 57 different pizza combinations possible.

Posted by

Irshad Anwar

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