Question

A certain pizza parlor has 7 different toppings. How many two- topping pizzas are possible?

Answer 1

Answer:

21

Step-by-step explanation:

Ok, so this may be confusing but I’ll explain.

Here is a very simplified diagram:

1-2, 1-3, 1-4, 1-5, 1-6, 1-7

2-3, 2-4, 2-5, 2-6, 2-7

3-4, 3-5, 3-6, 3-7

4-5, 4-6, 4-7

5-6, 5-7

6-7

*Note- I did this in about 30 seconds and on my phone so it is very simplified *

Each number, 1-7, is supposed to represent a different ingredient and they are put together to represent the two-ingredient combinations.

For example: 1-2 could represent pepperoni and sausage, and 1-5 could represent pepperoni and olives. This would mean that the 1 represents pepperoni, 2 represents sausage, and 5 represents olives.

If you count the number of combinations in each row, there are 21 combinations. This is because I made sure there are no repeats (2-3 AND 3-2) and because there wouldn’t be any doubles (1-1 or 2-2)