Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A pizza place offers 8 different toppings, but a customer can only choose a maximum of 5 toppings for their pizza. How many different pizza combinations are possible?  <div class='q

A pizza place offers 8 different toppings, but a customer can only choose a maximum of 5 toppings for their pizza. How many different pizza combinations are possible?
 

Option: 1

409


Option: 2

156


Option: 3

219


Option: 4

306


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: 0,1,2,3,4, or 5 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 8 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(8,2)=8 ! /(2 ! \times(8-2) !)=28.}

Case 4: 3 toppings:
Similarly, using the combination formula: \mathrm{C(8,3)=8 ! /(3 ! \times(8-3) !)=56.}

Case 5: 4 toppings:
Using the combination formula: \mathrm{C(8,4)=8 ! /(4 ! \times(8-4) !)=70.}

Case 6: 5 toppings:
Using the combination formula: \mathrm{C(8,5)=8 ! /(5 ! \times(8-5) !)=56.}

To find the total number of different pizza combinations, we sum the possibilities from all the cases:

\mathrm{1 ( 0 ~toppings )+8 ( 1~ topping )+28 ( 2~ toppings )+56 (3 ~toppings )+70(4~ toppings )+56(5~ toppings )= 219. }

Therefore, there are 219 different pizza combinations possible.

Posted by

Sanket Gandhi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE 2026: IIT admissions show major shift toward AI, data science, away from core engineering courses
anam-khan

JEE Main 2026: NIT Delhi cut-offs for BTech courses show ever-increasing demands for AI, computer skills
anam-khan

597 Eklavya school students clear JEE, NEET exams in 2024-25; Gujarat, MP lead

Latest Question