Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

A pizza place offers 3 different
cheeses and 8 different toppings. In how many ways can a pizza be made
with 1 cheese and 3 toppings?

Sagot :

kate200468
[tex]1\ cheese\ is\ choose\ from\ 3:\ \ \ {3 \choose 1} =3\\and\ 3\ toppings\ are\ choose\ from\ 8:\ \ \ {8 \choose 3} = \frac{8!}{3!\cdot(8-3)!}= \frac{5!\cdot6\cdot7\cdot8}{2\cdot3\cdot5!}=56 \\\\a\ pizza\ can\ be\ made\ on\ \ 3 \cdot 56=168\ \ ways[/tex]
AL2006
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.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.