Question

Can someone please answer. There is one problem. There's a picture. Thank you!

Answer 1

1 cheese from 3 cheeses

3 toppings from 8 toppings.

Number of ways: Note the order is irrelevant.

= ³C₁ * ⁸C₃

= 3/1 * 8*7*6/(3*2*1) = 3 * 56 = 168

Answer 2

The answer is D, or 168.
The cheese can be any one out of 3 = 3 choices. For each of those . . .
The first topping can be any one of 8. For each of those . . .
The second topping can be any one of the remaining 7 . For each of those . . .
The third topping can be any one of the remaining 6 .

Total number of ways to assemble a pizza = (3 x 8 x 7 x 6) = 1,008 ways.

BUT . . .

You could choose the SAME 3 toppings in (3 x 2) = 6 different ways, and
nobody could tell the difference once they were selected. All 6 different
ways would result in the same pizza.

So, out of the 1,008 total different ways there are of choosing ingredients,
there are only ( 1,008 / 6 ) = 168 different and distinct pizzas.