Grouping - combinatorics

In how many different ways can 24 people be divided into:

a) 6 groups of the same size.
b) Groups of 5, 6, 7, and 6 people.
c) Groups of 4, 5, 7, and 8 people.

Correct answer:

n₁ =  4096
n₂ =  9216
n₃ =  1536

Step-by-step explanation:

$$\begin{gathered} n=24 \\ k=4 \\ {n}_1=4^6=4096 \end{gathered}$$

$n_2=4^5\cdot 3^2\cdot 1^1=9216$

$n_3=4^4\cdot 3^1\cdot 2^1=1536$

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