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Poker
          Combinatorics
                                  or


                 How likely
                 is THAT?!?




Red Hot Poker by flickr user kimberlyfaye
The Binomial Theorem ...
   Algebraically




   Combinatorically




    Notice the patterns ...
(1) The coefficient of the term is:
(2) The exponent on a is given by: [n - (i - 1)]
(3) The exponent on b is given by: i - 1
(4) This relation holds for each term in the expansion:
                                             [exponent on a] + [exponent on b] = n
(5) The number of terms in any binomial expansion is: n + 1
Evaluate each term ...
                                    n!
                         nC r =
                                  (n-r)!r!
Pascal's Triangle
   Can you find the Hockey Stick pattern?
Any individual term, let's say the ith term, in a binomial expansion
can be represented like this:




 Example: Find the 4th term in the expansion of
Determine the indicated term in each expansion.

 (a) the 8th term in the expansion of
Example: Find the term that contains x7 in the expansion of
Find the term that contains   in the expansion of:
Find the term that contains   in the expansion of:

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Pre-Cal 40S May 12, 2009

  • 1. Poker Combinatorics or How likely is THAT?!? Red Hot Poker by flickr user kimberlyfaye
  • 2. The Binomial Theorem ... Algebraically Combinatorically Notice the patterns ... (1) The coefficient of the term is: (2) The exponent on a is given by: [n - (i - 1)] (3) The exponent on b is given by: i - 1 (4) This relation holds for each term in the expansion: [exponent on a] + [exponent on b] = n (5) The number of terms in any binomial expansion is: n + 1
  • 3. Evaluate each term ... n! nC r = (n-r)!r!
  • 4. Pascal's Triangle Can you find the Hockey Stick pattern?
  • 5. Any individual term, let's say the ith term, in a binomial expansion can be represented like this: Example: Find the 4th term in the expansion of
  • 6. Determine the indicated term in each expansion. (a) the 8th term in the expansion of
  • 7. Example: Find the term that contains x7 in the expansion of
  • 8. Find the term that contains in the expansion of:
  • 9. Find the term that contains in the expansion of: