Question

Buna. Am si eu nevoie de rezolvarea exercitiului 1, urgent. Va rog frumos, imi trebuie pana maine si nu stiu sa il fac . Dau funda.

Answer 1

$1) C^3_{7}= \frac{7!}{3!4!} = \frac{4!5*6}{6*4!}=5 \\ 2) C^6_{8}= \frac{8!}{6!*2!}= \frac{7*8}{2}=28 \\ 3) \frac{ C^3_{6}* P_{3} }{ A^2_{6} }= \frac{ \frac{6!}{3!*3!} *3!}{ \frac{6!}{4!} } = \frac{4*5*6}{5*6} =4 \\ 4) C^3_{8}+ \frac{ A^4_{9} }{ P_{4} } = \frac{8!}{3!*5!} + \frac{ \frac{9!}{5!} }{4!} =7*8+126=182 \\ 5) \frac{ A^6_{10}+ P_{10} }{7! C^6_{9} } = \frac{ \frac{10!}{4!}+10! }{7!* \frac{9!}{6!3!} }= \frac{10!( \frac{1}{4!}+1) }{9!* \frac{7}{6} } = \frac{10* \frac{25}{4} }{ \frac{7}{6} } =$=$= \frac{250}{4}* \frac{6}{7}= \frac{125}{2}* \frac{6}{7}= \frac{125*3}{7}= \frac{375}{7}$

Answer 2

1) $C_{7}^{3}$ = $\frac{n!}{k! * (n-k)!}$ = $\frac{7!}{3! * (7-3)! } = \frac{7!}{3!*4!} = \frac{5*6*7}{3!} = \frac{5*6*7}{1*2*3} =$ = 5 × 7 = 35
2) $C_{8}^{6} = C_{8}^{8-6} = C_{8}^{2} = \frac{8!}{2!*(8-2)!} = \frac{8!}{2!*6!} = \frac{7*8}{2!} = \frac{7*8}{1*2} =$ 7×4 = 28.
3) $\frac{ C_{6}^3*P_{3}}{A_{6}^{2}} = \frac{\frac{6!}{3!*3!}*3!}{ \frac{6!}{4!} } = \frac{ \frac{6!}{3!} }{ \frac{6!}{4!} } = \frac{6!}{3!} : \frac{6!}{4!} = \frac{6!}{3!} * \frac{4!}{6!} = \frac{4!}{3!} = 4$
4) $C_{8}^3 + \frac{A_{9}^4}{P_{4}} = \frac{8!}{3!*5!} + \frac{ \frac{8!}{5!} }{4!} = \frac{6*7*8}{3!} + \frac{8!}{5!*4!} = \frac{6*7*8}{1*2*3} + \frac{6*7*8}{4!} = 7*8 + \frac{6*7*8}{1*2*3*4}$ = 56 + 14 = 70
5) $\frac{A_{10}^6+P_{10}}{7!*C_{9}^6} = \frac{ \frac{10!}{4!} + 10! }{7!* \frac{9!}{6!*3!} } = \frac{10!( \frac{1}{4!} + 1 ) }{ 7*\frac{9!}{3!} } = \frac{10!( \frac{1}{4!} +1 ) }{ \frac{7*9!}{3!} } = 10! ( \frac{1}{4!} + 1 ) * \frac{3!}{7*9!} =$ = $10 ( \frac{1}{4!} + 1 ) * \frac{3!}{7} = 10 ( \frac{1}{24} + 1 ) * \frac{6}{7} = 10 * ( \frac{1}{24} + \frac{24}{24} ) * \frac{6}{7} = 10 * \frac{25}{24} * \frac{6}{7} = \frac{250}{28}$ = $\frac{125}{14}$

Sper sa-ti fie de folos, am incercat sa scriu cat mai explicit, te rog spune-mi daca ai vreo nelamurire la vreo rezolvare!