Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.