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