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In a pizza restaurant, you can get a basic pizza with two toppings, cheese and tomato. You can also make up your own pizza with extra toppings. You ca choose from four different extra toppings: olives, ham, mushrooms, and salami. Ross wants to order a pizza with different extra toppings. How many different combinations can Ross choose from?

Sagot :

sunflowwrgg

Answer: 9 different combinations (including ham +mushrooms + salami + olives)

Step-by-step explanation:

olives + ham + mushroom

olives + ham + salami

olives+ ham

olives+ salami

olives + mushrooms

ham +mushrooms

ham+ salami

salami + mushroom

You can use combinations to get to the total count of toppings you can make. Ross can make total of 15 different extra topping pizzas.

How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?

This can be done in total of [tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.

For this case, since there are 4 types of extra toppings available and Ross can take any number of toppings.

  • If he chooses to get only 1 topping, then total [tex]^4C_1 = 4[/tex] ways of getting such pizzas.
  • If he chooses to get 2 different toppings, then total [tex]^4C_2 = \dfrac{4 \times 3}{2 \times 1} = 6[/tex] ways.
  • If he chooses to get 3 different toppings, then total [tex]^4C_3 = \dfrac{4 \times 3 \times 2}{3 \times 2 \times 1} = 4[/tex] ways.
  • If he chooses to get 4 different toppings, then total [tex]^4C_4 = \dfrac{4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} = 1[/tex]  way.

Thus, in total there are 4+6+4+1 = 15 ways of getting pizzas with different extra toppings.

Thus, Ross can make total of 15 different extra topping pizzas.

Learn more about combinations here:

https://brainly.com/question/11958814

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