Question

Could you please answer this Permutation & Combination Question?

In a pizza resturant, you get a basic pizza with two toppings, cheese and tomato. You can also make up your own pizza with extra toppings. You can also choose from 10 different toppings, e.g. olives, ham, mushroom, salami etc. Ross wants to order a pizza with 2 different extra toppings. How many different combinations are possible?

Answer 1

\[\dbinom{10}{2}\]
\[=\frac{10\times 9}{2}=5\times 9=45\]

Answer 2

btw we don't need a formula for this. 10 choices for first topping, times 9 choices for second. and since (ham, olive) is the same as (olive, ham) we divide by 2

Answer 3

oh okay, thankyou very much. =)