Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » discretemath

Topic: Combinations Problem
Replies: 2   Last Post: Nov 20, 2010 11:35 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
ChrisPy

Posts: 3
Registered: 9/27/08
Combinations Problem
Posted: Nov 20, 2010 11:03 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I am studying for the GRE and reviewing a fair amount of pre-college math. I have a problem involving combinations, and have worked out a solution that I want to check on this forum. I've put my answer below, so just look at the question if you want to try it for yourself. Let me know if there is a faster way to do this too, please.


===== QUESTION =====

Anne and Mark want to invite 5 friends to a dinner party. Anne has 7 friends, and Mark as 6 friends. They have no friends in common. If each of them must have at least 2 friends at the party, how many combinations of guests are possible?





===== MY ANSWER ======

Find the total possible combinations and then subtract those that do not meet the two friend each criteria...

13C5 = 1287 (Total possible combos)
--- Invalid Combos ---
7C4 * 6C1 = 210 (Combos with 4 of Anne's friends, but only one of Mark's)
6C4 * 7C1 = 105 (Combos with 4 of Mark's friends but only one of Anne's)
7C5 = 21 (Combos with just Anne's friends)
6C5 = 6 (Combos with just Mark's friends)

So we subtract the invalid possibilities from total possibilities, and get 945.

BONUS: What if they had one friend in common?

Thanks in advance for any help.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.