1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculate the amount of ways 4 prizes can be awarded to 12 students

  1. Nov 11, 2009 #1
    calculate the amount of ways 4 prizes can be awarded to 12 students if:
    a)each student cannot recieve more than one prize
    b)each student may recieve more than one prize
    c)at least one student recieves more than one prize

    a)
    1st prize -> 12 possibilities
    2nd prize -> 11 possibilities
    3rd prize -> 10 possibilities
    4th prize -> 9 possibilities

    12*11*10*9 = 11880

    b)
    1st prize -> 12 possibilities
    2nd prize -> 12 possibilities
    3rd prize -> 12 possibilities
    4th prize -> 12 possibilities

    12*12*12*12 = 20736

    c)
    1st prize -> 12 possibilities
    2nd prize -> 11 possibilities
    3rd prize -> 10 possibilities
    4th prize -> 3 possibilities (the student who won the 1st/2nd/3rd prize)

    12*11*10*3=3960

    but the correct answer is 8856, which happens to be the subtraction of the answer to b) from the answer to a), why is this the way to solve c) ?? is there not any other way?
     
  2. jcsd
  3. Nov 11, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: combinatorics

    How about the case where two students get two prizes each? Can you think of some other ways of awarding the prizes your counting doesn't include?
     
  4. Nov 11, 2009 #3
    Re: combinatorics

    now that i look at if after a bit of a break from it, it just seems so obvious, i have b)all the possibilities, and a) the possibilities where nobody wins more than 1 prize, all i need to do is subtract. thanks anyway
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Calculate the amount of ways 4 prizes can be awarded to 12 students
  1. Ways of calculating e (Replies: 7)

Loading...