A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two course meal?

Question

whpalmer4 · Answer

You choose an appetizer, then you choose a main course.  You've got a choice of 10 appetizers, and after each one you have a choice of 7 main courses.  If you order appetizer #1, you can then order main course #1, #2, #3, #4, #5, #6, or #7, so that's 7 different ways just with the first appetizer choice.  If you do that for all of them, how many do you get?

anonymous · Answer

7*7*7*7*7*7*7 ???

anonymous · Answer

im confused

whpalmer4 · Answer

No.  Think about it a bit more.  What if you had 2 appetizers (A, B) and 3 main courses (1,2,3)?  You could start out with appetizer A:

A,1
A,2
A,3
or appetizer B:
B, 1
B, 2
B, 3

so there would be 6 different meals, right?  Wasn't it just the number of choices for the first course * the number of choices for the second course?

anonymous · Answer

soo.... then would it be:

A, 1
A, 2
A, 3
A, 4
A, 5
A,6
A, 7

etc... ?

yrelhan4 · Answer

do you have any idea about combinations and permutations?

anonymous · Answer

no this is just probability

campbell_st · Answer

its simply 10 times 7 ways... its called the fundemental theorem of counting

anonymous · Answer

that's what i thought from the start, but on a previous problem i got it wrong @campbell_st

campbell_st · Answer

well it depends on the conditions... but this is really straight forward... multiply the choice in each course... 

glad to help

anonymous · Answer

okay makes sense thank you @campbell_st

anonymous · Answer

wait i read the problem again.  even if the question is asking for 2 course meals and 10 appetizers and 7 main courses, would the answer still be 70?

anonymous · Answer

cause if you just multiply 10 and 7 thats 70, but its 2 course meals each.... sooo do you double it? thats when i get confused. @campbell_st

campbell_st · Answer

nope... its simply 70 you can prove it with a tree diagram 

this is what it would look like at the start if you had a large piece of paper

|dw:1362037385630:dw|

hope this makes sense.

anonymous · Answer

OH!!!!!!  yeah that totally makes sense!

anonymous · Answer

thank you so much!

anonymous · Answer

@campbell_st

campbell_st · Answer

glad to help... obviously you are doing permutations, combinations and counting techniques...

anonymous · Answer

yeah,its an online class so they just give us like "worksheets" and then i have to teach myself everything

anonymous · Answer

Yo You Got this!!

anonymous · Answer

thank you everyone!!! i got them right!!