1) [tex] C_{7}^{3} [/tex] = [tex] \frac{n!}{k! * (n-k)!} [/tex] = [tex] \frac{7!}{3! * (7-3)! } = \frac{7!}{3!*4!} = \frac{5*6*7}{3!} = \frac{5*6*7}{1*2*3} = [/tex] = 5 × 7 = 35
2) [tex] C_{8}^{6} = C_{8}^{8-6} = C_{8}^{2} = \frac{8!}{2!*(8-2)!} = \frac{8!}{2!*6!} = \frac{7*8}{2!} = \frac{7*8}{1*2} = [/tex] 7×4 = 28.
3) [tex] \frac{ C_{6}^3*P_{3}}{A_{6}^{2}} = \frac{\frac{6!}{3!*3!}*3!}{ \frac{6!}{4!} } = \frac{ \frac{6!}{3!} }{ \frac{6!}{4!} } = \frac{6!}{3!} : \frac{6!}{4!} = \frac{6!}{3!} * \frac{4!}{6!} = \frac{4!}{3!} = 4 [/tex]
4) [tex] C_{8}^3 + \frac{A_{9}^4}{P_{4}} = \frac{8!}{3!*5!} + \frac{ \frac{8!}{5!} }{4!} = \frac{6*7*8}{3!} + \frac{8!}{5!*4!} = \frac{6*7*8}{1*2*3} + \frac{6*7*8}{4!} = 7*8 + \frac{6*7*8}{1*2*3*4} [/tex] = 56 + 14 = 70
5) [tex] \frac{A_{10}^6+P_{10}}{7!*C_{9}^6} = \frac{ \frac{10!}{4!} + 10! }{7!* \frac{9!}{6!*3!} } = \frac{10!( \frac{1}{4!} + 1 ) }{ 7*\frac{9!}{3!} } = \frac{10!( \frac{1}{4!} +1 ) }{ \frac{7*9!}{3!} } = 10! ( \frac{1}{4!} + 1 ) * \frac{3!}{7*9!} =[/tex] = [tex]10 ( \frac{1}{4!} + 1 ) * \frac{3!}{7} = 10 ( \frac{1}{24} + 1 ) * \frac{6}{7} = 10 * ( \frac{1}{24} + \frac{24}{24} ) * \frac{6}{7} = 10 * \frac{25}{24} * \frac{6}{7} = \frac{250}{28} [/tex] = [tex] \frac{125}{14} [/tex]
Sper sa-ti fie de folos, am incercat sa scriu cat mai explicit, te rog spune-mi daca ai vreo nelamurire la vreo rezolvare!
