Question

ajutatima va rog la matematica multumesc

Answer 1

Exercitiul 1

$\frac{(n-4)!}{(n-2)!}= \frac{(n-2)!(n-3)(n-4)}{(n-2)!} = n^2-4n-3n+12 = n^2-7n+12$

Exercitiul 2

$C_{7}^{5}= \frac{7!}{5!2!} = \frac{5!*6*7}{5!*2!}= \frac{42}{2}=12$

$P7=7!=1*2*3*4*5*6*7=5040$

$A_{7}^{5}= \frac{7!}{(7-5)!} = \frac{7!}{2!}= \frac{2!*3*4*5*6*7}{2!} = 2520$

Exercitiul 4

[tex] \frac{A_{15}^{5}+A_{15}^{6}}{A_{15}^{4}}= \frac{ \frac{15!}{10!} + \frac{15!}{9!} }{ \frac{15!}{11!} }= [/tex]
[tex] \frac{ \frac{10!*11*12*13*14*15}{10!} + \frac{9!*10*11*12*13*14*15}{9!} }{ \frac{11!*12*13*14*15}{11!} } = \frac{360360+3603600}{32760}= 121[/tex]