Factorials
What is
0!
1
What is
\sum_{i=1}^3 i
6
How many ways can I arrange 4 different socks?
4!=24
Find
3P2
6
What is the third row of Pascals triangle?
1 3 3 1
Simplify
\frac{8!}{8!}
1
What is
\sum_{m=1}^2 m^2
5
How many different ways can I arrange 3 books picking 2 at a time? ORDER DOES NOT MATTER.
3C2=3
Find
3P0
1
Expand using the binomial theorem
(2x+1)^2
***Check correct work
4x^2+4x+1
Simplify
\frac{8!}{7!}
8
What is
\sum_{k=1}^2 (2k+1)
8
Now I have four books and want to pick 1 at a time but order MATTERS. How many ways can I combine them.
4P1=24
Find
3P1
3
What is the first term in the binomial theorem expansion of
(x+a)^3
((3),(0))(x)^{3-0}(a)^0
Simplify
\frac{4!}{2!}
12
What is
\sum_{i=1}^3 -i^2
15
How many different ways can I arrange 2 books picking 3 at a time?
Undefined
Find
3P9
Undefined!
What is the precise statement of the Binomial theorem?
((n),(k))=nCk
Simplify
\frac{4!}{2!2!}
6
What is
\sum_{k=1}^3 (-1)^kk
-2
There are 9 supreme court justices. Each shakes each others hand ONCE. How many handshakes are there in total?
36
Find
4C3
4
Show that the binomial theorem is true for
n=2
***Check for correct argument i.e. matching up binomial coefficient with combinations.