Question

помогите с алгеброй! (30 баллов)
не просто ответьт, а как и решали

Answer 1

Объяснение:

$\displaystyle\\1)\\\\\frac{A_{15}^4+A_{14}^5}{A_{15}^3} =\frac{\frac{15!}{(15-4)!}+\frac{14!}{(14-5)!} }{\frac{15!}{(15-3)!} } =\frac{\frac{11!*12*13*14*15}{11!}+\frac{9!*10*11*12*13*14}{9!} }{\frac{12!*13*14*15}{12!} } =\\\\\\=\frac{12*13*14*15+10*11*12*13*14}{13*14*15} =\frac{13*14*(12*15+10*11*12)}{13*14*15} =\\\\=\frac{12*15+10*11*12}{15} =\frac{180+1320}{15} =\frac{1500}{15} =100.$

$\displaystyle\\2)\\\\\frac{A_{12}^4*P_7}{A_{11}^9} =\frac{\frac{12!}{(12-4)!}*7! }{\frac{11!}{(11-9)!} }=\frac{\frac{8!*9*10*11*12}{8!}*7! }{\frac{2!*3*4*5*6*7*8*9*10*11}{2!} }=\frac{9*10*11*12*7!}{3*4*5*6*7*8*9*10*11} =\\\\=\frac{12*7!}{3*4*5*6*7*8} =\frac{1*2*12*7!}{1*2*3*4*5*6*7*8} =\frac{24*7!}{7!*8} =\frac{24}{8} =3.$