I am searching for the proof of the multinomial coefficients formula (formula in the picture)
Any help please?
I am searching for the proof of the multinomial coefficients formula (formula in the picture)
Any help please?
They are all just different forms of the multinomial coefficient.
Since there are $m_i$ repetitions of $x_i$, with $\sum m_i = n$, using the formula for permutations with repetitions, we immediately get
$\dfrac{n!}{m_1!m_2!...m_i!}$, but more usually written as $\dbinom{n}{m_1,m_2,...m_i}$
You should be able to see that the other two forms are also the same formula presented differently.