Question

A fast-food restaurant offers 7 different burgers, 5 different side orders, 8 different flavor drinks, and 8 different flavors of ice cream. in how many ways can a combo containing 3 burgers, 2 different sides, 3 different flavor drinks, and 2 ice cream flavors be made?

Answer 1

548800.
Use the fundamental counting principle and combinations formula to find the total possibilities. use combinations to find the combos then multiply each set of possibilities together.

7 nCr 3 = 35 hamburgers combo possibilities.
5 nCr 2 = 10 sides combo possibilities
8 nCr 3 = 56 drinks combo possibilities
8 nCr 2 = 28 ice cream combo possibilities

Multiply each possibility together to get total possibilities.
35*10*56*28 = 548800

Answer 2

The number of ways can a combo containing 3 burgers, 2 different sides, 3 different flavor drinks, and 2 ice cream flavors are made is 548,800.

What are permutation and combination?

A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

A fast-food restaurant offers 7 different burgers, 5 different side orders, 8 different flavor drinks, and 8 different flavors of ice cream.

The number of ways can a combo containing 3 burgers, 2 different sides, 3 different flavor drinks, and 2 ice cream flavors be made will be

$\rm Number \ of \ way = \ ^7C_3 * ^5C_2 *^8C_3*^8C_2\\\\\\Number \ of \ way = \ \dfrac{7!}{(7-3)!*3!} *\dfrac{5!}{(5-2)!*2!}*\dfrac{8!}{(8-3)!*3!}*\dfrac{8!}{(8-2)!*2!}\\\\\\Number \ of \ way = \ \dfrac{7*6*5*4!}{4!*3*2*1} *\dfrac{5*4*3!}{3!*2*1} * \dfrac{8*7*6*5!}{5!*3*2*1} *\dfrac{8*7*6!}{6!*2*1}\\\\\\Number \ of \ way = \ \dfrac{7*6*5}{3*2*1} *\dfrac{5*4}{2*1} * \dfrac{8*7*6}{3*2*1} *\dfrac{8*7}{2*1}\\\\\\Number \ of \ way = \ 35*10*56*28\\\\Number \ of \ way = \ 548,800$

The number of ways is 548,800.

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255