[Verse 1]
When you've got more than just two terms to raise
To a power that's n, don't be amazed
X one plus x two plus terms galore
The multinomial opens up the door
[Chorus]
Multinomial, expand it all
N factorial leads the call
Divide by k factorials below
Where k one plus k two makes n, you know
Count the ways to split and share
Objects grouped with loving care
[Verse 2]
Start with n objects in your hand
Partition them across the land
K one goes here, k two goes there
Each group gets its rightful share
[Chorus]
Multinomial, expand it all
N factorial leads the call
Divide by k factorials below
Where k one plus k two makes n, you know
Count the ways to split and share
Objects grouped with loving care
[Bridge]
Every term needs its own power
X to the k in its finest hour
Sum all combinations that add up right
K values totaling n in sight
[Verse 3]
Coefficients tell the tale
How many ways will never fail
To arrange your objects neat and clean
In groups of every size you've seen
[Chorus]
Multinomial, expand it all
N factorial leads the call
Divide by k factorials below
Where k one plus k two makes n, you know
Count the ways to split and share
Objects grouped with loving care
[Outro]
From binomial we've grown so wide
With m terms standing side by side
The theorem shows us how to count
Every way that will amount