Question

Помогит найти: решите Пожалуйста

Answer 1

$1)A_{15}^{3} =\frac{15!}{(15-3)!} =\frac{12!*13*14*15}{12!}=13*14*15=\boxed{2730}\\\\\\2)C_{5}^{3}=\frac{5!}{3!*(5-3)!} =\frac{3!*4*5}{3!*1*2}=\frac{4*5}{2}=10\\\\C_{5} ^{2} =\frac{5!}{2!*(5-2)!} =\frac{5!}{2!*3!}=\frac{3!*4*5}{1*2*3!}=\frac{4*5}{2}=10\\\\A_{5}^{2}=\frac{5!}{(5-2)!}=\frac{5!}{3!}=\frac{3!*4*5}{3!}=20\\\\\frac{C_{5} ^{3}-C_{5}^{2}}{A_{5}^{2}}=\frac{10-10}{20} =\boxed0$

Answer 2

Объяснение:

$A_{15}^3=\frac{15!}{(15-3)!} =\frac{12!*13*14*15}{12!}=13*14*15=2730.\\\frac{C_5^3-C_5^2}{A_5^2}=\frac{\frac{5!}{(5-3)!*3!} -\frac{5!}{(5-2)!*2!} }{\frac{5!}{(5-2)!} } =\frac{\frac{3!*4*5}{2!*3!} -\frac{3!*4*5}{3!*2!} }{\frac{3!*4*5}{3!} } =\frac{\frac{20}{1*2}-\frac{20}{1*2} }{20}=\frac{10-10}{20}=\frac{0}{20}=0.$