Math 4X Quiz 8.2 Review:
-
Know how to calculate probabilities (this is vague, but look at all of your old probability
assignments – it’s all fair game on the quiz)
Know how to work algebraically with combinations (getting common denominators with
factorials, etc.)
Use the binomial expansion theorem to:
o completely expand binomials
o determine the coefficient of a specific term
o determine specific terms
Know basic identities involving Pascal’s Triangle and/or how to prove them:
o Sums of rows
o Hockey Stick (like #18 in the homework assignment) – see below.
o Other identities based on combinations located in the triangle
-
-
The “hockey stick identity,” as it’s become known, is
demonstrated at right – note that:
, or ( )
( )
( )
( )
( )
(
)
(
)
(
( ) (in red).
( )
( )
( )
(
)
(
) (in green).
) (in blue).
Basically – start at one edge of the triangle … the sum of the entries along that “column” is found in the
next row and to the right (if coming from the right edge) and to the left (if coming from the left edge).
In general, ( )
(
)
( )
(
)
(
)
(
)
(
(
)
(
)
(
) (from the right), or
) (from the left).
But don’t memorize these!! It’s much more effective for you to see how they work in the triangle and
then recreate the combinations if you need to.