Probability: Permutations and Combinations

Date: 12/10/2002 at 20:27:26
From: Apurva Yeluru
Subject: Probability: Permutations and Combinations

Dr. Math,

I am in eighth grade. We are not doing probability but I am interested 
in it. Last year in our school, we had a probability fair and I could 
not understand it very well. Now I can! I know what probability is and 
what permutations are and what combinations are. But this is the part 
where I am stuck: How is probability related to permutations and 
combinations? 

I would be delighted if you replied.

Thanks!

Date: 12/11/2002 at 11:50:25
From: Doctor Ian

Hi Apurva,

The relationship is that when you want to compute the probability that
something will happen, you do this:

      how many ways can the thing happen?
  p = -----------------------------------
      how many ways can anything happen? 

Combinations and permutations are useful for computing the numerator
and denominator of this fraction. For example, if you want to know
the probability of drawing two pairs in poker, that's 

      the number of combinations of 5 cards with 2 pairs
  p = --------------------------------------------------
      the number of combinations of 5 cards

In other words, when you're computing probabilities, you often need to
compute the number of ways that things can be selected from a group
(combinations) or ordered within a group (permutations). 

Does that make sense? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 12/14/2002 at 09:57:29
From: Apurva Yeluru
Subject: Thank you (Probability: Permutations and Combinations)

Doctor Ian,

Thank you for the answer. It really does make sense. 
Now I think I can solve some problems!

Apurva