Answer:
800
Step-by-step explanation:
Answer:
468 ways
Step-by-step explanation:
Given: A catering service offers 5 appetizers, 4 main courses, and 8 desserts
To find: number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts.
Solution:
A permutation is an arrangement of elements such that order of elements matters and repetition is not allowed.
Number of appetizers = 5
Number of main courses = 4
Number of desserts = 8
Number of ways of choosing k terms from n terms = ![nPk=\frac{n!}{(n-k)!}](https://tex.z-dn.net/?f=nPk%3D%5Cfrac%7Bn%21%7D%7B%28n-k%29%21%7D)
Number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts = ![5P4+4P2+8P3](https://tex.z-dn.net/?f=5P4%2B4P2%2B8P3)
![=\frac{5!}{(5-4)!}+\frac{4!}{(4-2)!}+\frac{81}{(8-3)!}\\=5!+\frac{4!}{2!}+\frac{8!}{5!}\\=5!+(4\times 3)+(8\times 7\times 6)\\=120+12+336\\=468](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%21%7D%7B%285-4%29%21%7D%2B%5Cfrac%7B4%21%7D%7B%284-2%29%21%7D%2B%5Cfrac%7B81%7D%7B%288-3%29%21%7D%5C%5C%3D5%21%2B%5Cfrac%7B4%21%7D%7B2%21%7D%2B%5Cfrac%7B8%21%7D%7B5%21%7D%5C%5C%3D5%21%2B%284%5Ctimes%203%29%2B%288%5Ctimes%207%5Ctimes%206%29%5C%5C%3D120%2B12%2B336%5C%5C%3D468)
So, this can be done in 468 ways.
Mathematically, a ray is a portion of a line which starts at a point and goes off in a particular direction to infinity.
The answer must be -52 because I added parenthesis around -3 × 6 so it won't confuse people. I multiplied -3 and 6 and got -18. Then I multiplied -18 and 3 and got -54. I add -54 and 2 and got -52. Since there's more of negative than positive, I subtracted and got -52. Hope this helps :)