A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

MEDAL!! (suppose there is a group of 7 people from which we will make a committee) In how many ways can we pick a three-person committee?

  • This Question is Closed
  1. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Let's say we have 3 slots A,B,C how many do we have to choose from for slot A?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    7?

  3. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Correct, then for slot B?

  4. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Recall that one of the sever is already in slot A.

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6?

  6. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yep, and then C?

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    multiply?

  9. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, you'll multiply 7, 6 and 5

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    210

  11. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that won't be your final answer but it gets you closer

  12. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    210 is the number of ways to pick 3 people IF order mattered but there is no ranking on this committee, so order doesn't matter

  13. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so what you have to do is divide by 3! = 3*2*1 = 6 to get the correct count

  14. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the reason why is because there are 6 ways to order any three objects xyz xzy yxz yzx zxy zyx

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    210 divided by 3?

  16. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    210/6 actually

  17. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    or 210/(3!)

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay. I read your response wrong haha so 35

  19. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    correct

  20. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    another way is to use the combination formula \[\Large _n C _r = \frac{n!}{r!*(n-r)!}\] with n = 7 and r = 3 and you'll get the same answer

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910 what if it was a four-person committee instead? wouldn't it be 7C4=35? also?

  22. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that is correct

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you

  24. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    if you think of it in terms of 7 slots A through G we have this |dw:1441932178631:dw|

  25. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    now imagine cutting a line through that group such that one side (say the left side) has 3 slots and the other side has 4 slots |dw:1441932241059:dw|

  26. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    arranging 7 people to go in slots A through C is the exact same as arranging the remaining 4 to go in D through G so that's why 7 C 3 = 7 C 4 in general \[\LARGE _n C _x = \ _n C _y\] where x+y = n (so in this case, x+y = 3+4 = 7 which is the value of n)

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, that is the way my instructor explains it also, thanks again!

  28. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you're welcome

  29. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.