Working with the binomial theorem.

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: