Question

combinari de 5 luate cate 4 + aranjamente de 5 luate cate 4

Answer 1

$\displaystyle \mathtt{C_5^4+A_5^4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boxed{\mathtt{\mathbf{C_n^k= \frac{n!}{(n-k)! \cdot k!} }}}}~\\ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boxed{\mathtt{\mathbf{A_n^k= \frac{n!}{(n-k)!} }}} \\ \\ \mathtt{C_5^4= \frac{5!}{(5-4)!\cdot 4!} = \frac{4! \cdot 5}{1! \cdot 4!}=5 }\\ \\ \mathtt{A_5^4= \frac{5!}{(5-4)!}= \frac{5!}{1!} =1 \cdot 2 \cdot 3 \cdot 4 \cdot 5= 120}\\ \\ \mathtt{C_5^4+A_5^4=5+120=125}\\ \\ \mathtt{\mathbf{C_5^4+A_5^4=\underline{125}}}$