Permuatations and Combinations Lesson 6

Review:

1)Provide students with a pathways problem:
2) Create a word where the number of different arrangements is 8!/(3!5!)
3) If you invited 5 people to your party but forgot to ask them to RSVP, how many different arrangements are possible?

This last question is the key to linking past knowledge to new knowledge.

Next show the video:

Then create a plinko board on the board and ask the students to determine the number of ways for the plinko to fall.  Assuming:
1) The Plinko does not come back up
2) It either falls left or right.
(They should create the first couple of rows of Pascal's triangle)

Create enough rows to row 6 (the answer to the last question in the review).  Rewrite the last row in Combination notation instead of numeral notation.

Next, ask them to expand
(x+y)^0, (x+y)^1..., (x+y)^3.  (They should be getting irritated at this point).

Now, ask if they notice a pattern here...linking the co-efficients to the Pascal's Triangle.
Observations:
(x+y)^n has n+1 terms, uses the n+1 row of the triangle, and will have co-efficients of nC0, nC1,...,nCn

Depending on time you can create the binomial theorem with them or just state it:
tk+1=nCk(x)^(n-k)y^k

Now give them some questions:
Determine the ___ term of the expansion (__+___)^___ , where the blanks can be various numbers and variables.