← Topic 3 · Counting & Probability
AMC 10/12 · Cheatsheet
Topic 3 · Counting & Probability
Chapter 2 · Counting principles, perms & combs
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Product / sum rule
AND
⇒
×
,
OR
⇒
+
\text{AND}\Rightarrow\times,\;\; \text{OR}\Rightarrow +
AND
⇒
×
,
OR
⇒
+
Permutations
n
P
r
=
n
!
(
n
−
r
)
!
{}_nP_r = \tfrac{n!}{(n-r)!}
n
P
r
=
(
n
−
r
)!
n
!
Combinations
(
n
r
)
=
n
!
r
!
(
n
−
r
)
!
=
n
P
r
r
!
\binom{n}{r} = \tfrac{n!}{r!(n-r)!} = \tfrac{{}_nP_r}{r!}
(
r
n
)
=
r
!
(
n
−
r
)!
n
!
=
r
!
n
P
r