Combinations: A woman has 11 close friends, and wants to invite some for dinner.

[Ujandja]

Please help me with this question?

A woman has 11 close friends:
a) In how many ways can she invite 5 of them to dinner?
b) In how many ways can she invite 5 of them to dinner if
i) 2 of them are a couple and will not attend separately?
ii) there are 2 who are not on good terms and at most only one of them can be invited?

*The problem I have with this question is that the asker does not specify which five of the eleven in part b) can be invited and I don't even know how one invitation to dinner combination would look like, I'm at a loss as to how to approach this. Please help!

THANKS FOR THE HELP EVERYONE IT WAS JUST MY UNDERSTANDING OF THE ENGLISH THAT WAS OFF BECAUSE I ASSUMED THAT THEY EACH HAD TO BE INVITED ONE BY ONE! I KNOW WHAT TO DO NOW, THANKS!

 

[tkhunny]

Please help me with this question?

A woman has 11 close friends:
a) In how many ways can she invite 5 of them to dinner?
b) In how many ways can she invite 5 of them to dinner if
i) 2 of them are a couple and will not attend separately?
ii) there are 2 who are not on good terms and at most only one of them can be invited?

*The problem I have with this question is that the asker does not specify which five of the eleven in part b) can be invited and I don't even know how one invitation to dinner combination would look like, I'm at a loss as to how to approach this. Please help!

#1 Decide if "order matters". Is "Steve and Margaret" a different invitation from "Margaret and Steve"?
#2 b1 is a favorite. Just tape them together with duct tape and now you have only 10 friends. (That's almost as complicated as it is.)

Let's see your work on the matter, shall we? You can't have NO idea. Give us something to go on.

 

[mmm4444bot]

… The problem I have with this question is that the asker does not specify which five of the eleven in part b) can be invited …

The question does not ask "which five" can be invited. It's asking you to count the possibilities.

… I don't even know how one invitation to dinner combination would look like …

They're not asking you to describe what any particular combination looks like. They're asking you to count them.

If you need to see what combinations look like, you could write out simpler examples. How many ways can you invite two people from a collection of four people? Start by naming the four people: A, B, C, D

Here is what the possible combinations (two objects chosen from a set of four objects) look like:

AB
AC
AD
BC
BD
CD

How many ways? The answer is six.

If A and B are a couple who will not be separated, then the possibilities look like this:

AB
CD


Are you in a math class? Have you learned any formulas? If you have a textbook, look at the index for these topics: factorial, counting principles, permutation, combination.

If you don't have a textbook, google keywords permutations combinations. There are lots of free lessons on the Internet; here are two sites:

http://www.coolmath.com/algebra/20-combinatorics

https://www.mathsisfun.com/combinatorics/combinations-permutations.html

After you have studied some lessons and examples, try your exercise again.


Without seeing your attempts, it's hard for us to guess where you're stuck. :cool:

 

[pka]

A woman has 11 close friends:
a) In how many ways can she invite 5 of them to dinner?
b) In how many ways can she invite 5 of them to dinner if
i) 2 of them are a couple and will not attend separately?
ii) there are 2 who are not on good terms and at most only one of them can be invited?

In b i) We can answer \(\displaystyle \dbinom{9}{3}+\dbinom{9}{5}\) Can you explain the sum? What is being added?

In b ii) We can answer \(\displaystyle \dbinom{11}{5}-\dbinom{9}{3}\) Can you explain the difference sign? Why is this at most one?