Explicație pas cu pas:
aranjamente și combinări
[tex]\boxed {A_{n}^{k} = \frac{n!}{(n-k)!} } \: \boxed {C_{n}^{k} = \frac{n!}{k! \cdot (n-k)!} }[/tex]
unde:
[tex]\boxed {1 \cdot 2 \cdot 3 \cdot ... \cdot n = n!} \: \boxed {(n - 1)! \cdot n = n!}[/tex]
[tex]A_{5}^{2} \cdot C_{6}^{2} \cdot A_{4}^{2} = \frac{5!}{(5 - 2)!} \cdot \frac{6!}{2!(6 - 2)!} \cdot \frac{4!}{(4 - 2)!} = \\ = \frac{5!}{3!} \cdot \frac{6!}{2!4!} \cdot \frac{4!}{2!} = \frac{ \not3! \cdot 4 \cdot 5}{\not3!} \cdot \frac{\not4! \cdot 5 \cdot 6}{1 \cdot 2 \cdot \not4!} \cdot \frac{\not2! \cdot 3 \cdot 4}{\not2!} \\ = {3}^{2} \cdot {4}^{2} \cdot {5}^{2} = \bf {60}^{2} [/tex]
q.e.d.
