Question

Fat Kat's offers a special on large two topping pizzas. In how many different ways can you order a two topping pizza if you can choose from 18 toppings? NO LINKS!!!​

Answer 1

Answer:   153

=======================================================

Explanation:

There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.

If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.  

So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations

------------------------

The alternative method involves using the nCr combination formula

Use n = 18 and r = 2 in this formula

$_n C _r = \frac{n!}{r!*(n-r)!}$

the exclamation marks indicate factorial.

Answer 2

Answer:

in 9 different ways.

Step-by-step explanation:

divide 18 by 2 and u would get the answer