Probability and Combinations

Key Questions

  • How do permutations and combinations differ?

    A permutations is an arrangement, so the order of its elements matters; on the other hand, a combination is a subset, so the order of its elements does not matter.

    Example

    All permutations of two elements from #{a,b,c}# are:

    #ab, ba, ac,ca, bc#, and #cb#

    All combinations of two elements from #{a,b,c}# are:

    #{a,b}, {a,c}#, and #{b,c}#

    I hope that this was helpful.

    Wataru · 1 · Nov 24 2014
  • How do you calculate combinations of numbers in word problems?

    I need more details to answer this question. This is a video my co-teacher and I made. Hope it helps, if not please give me some details and I will try to do better.
    http://www.frontporchmath.com/topic/probability-using-tree-diagram-bagel-grab-bag/

    Lea · 1 · Feb 24 2015
  • How do you calculate combinations of things?

    Combinations of items are basically subsets of the items, so the number of combinations is the number of subsets of items.

    Let #C(n,r)# denote the number of combinations of #n# item chosen #r# items at a time. Then, it can be found by

    #C(n,r)={P(n,r)}/{r!}={n cdot (n-1) cdot (n-2) cdot cdots cdot (n-r+1)}/{r!}={n!}/{(n-r)! r!}#

    Example

    Find the number of ways to choose 3 cookies out of 6 distinct cookies.

    #C(6,3)={P(6,3)}/{3!}={6cdot5cdot4}/{3cdot2cdot1}=20#

    Hence, there are 20 ways to choose 3 cookies from 6 cookies.

    I hope that this was helpful.

    Wataru · 1 · Oct 31 2014

Questions

Systems of Equations and Inequalities