Question

In a pizza restaurant ,one can get a basic pizza with two toppings :

cheese and tomato. You can also make up pizza with extra toppings.

You can choose from four different extra toppings: olives, ham,

mushrooms and salami. Rajesh wants to order a pizza with two

different extra toppings.

How many combinations can Rajesh

choose from?
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Answer 1

Answer:

6 combinations

Step-by-step explanation:

Answer 2

Answer:

The number of combinations that can be made is 6.

Step-by-step explanation:

Combination:

• A combination in mathematics refer to the technique of determining the number of possible arrangements can be done in a set of n items.
• Here, the order of the selection does not matter and selection is not repeated.
• The formula for combination is given by

        $C(n,r)=^{n} C_{r} =\dfrac{n!}{r!(n-r)!}$

• where n is the total number of elements in a set, r is the number of selected objects.

Given a basic pizza with two toppings.

The number of different extra toppings on pizza offered, n = 4

The number of toppings chosen by Rajesh, r = 4

Substituting in the above formula,

$C(4,2)=^{4} C_{2} =\dfrac{4!}{2!(4-2)!}$

                     $=\dfrac{4!}{2!(2)!}=\dfrac{4\times3\times2\times1}{2\times1\times2\times1}$

                    $=3\times2=6$

Therefore, the number of combinations that can be made is 6.

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