\(C_{y+8}^{y+3}=5\cdot A_{y+6}^3\)
=>\(\frac{\left(y+8\right)!}{\left(y+8-y-3\right)!\cdot\left(y+3\right)!}=5\cdot\frac{\left(y+6\right)!}{\left(y+6-3\right)!}\)
=>\(\frac{\left(y+8\right)\left(y+7\right)\left(y+6\right)\left(y+5\right)\left(y+4\right)}{5!}=5\cdot\left(y+6\right)\left(y+5\right)\left(y+4\right)\)
=>(y+8)(y+7)/5!=5
=>(y+8)(y+7)=5!*5=120*5=600
=>\(y^2+15y+56-600=0\)
=>\(y^2+15y-544=0\)
=>(y+32)(y-17)=0
=>y=-32(loại) hoặc y=17(nhận)
\(A_{y+1}^4+3\cdot C_{y}^3\)
\(=A_{18}^4+3\cdot C_{17}^3\)
\(=\frac{18!}{\left(18-4\right)!}+3\cdot\frac{17!}{\left(17-3\right)!\cdot3!}\)
\(=18\cdot17\cdot16\cdot15+3\cdot\frac{17!}{14!\cdot3!}=18\cdot17\cdot16\cdot15+3\cdot\frac{17\cdot16\cdot15}{6}\)
\(=18\cdot17\cdot16\cdot15+\frac12\cdot17\cdot16\cdot15\)
\(=18\cdot17\cdot16\cdot15+17\cdot8\cdot15=17\cdot15\cdot8\cdot\left(18\cdot2+1\right)=17\cdot15\cdot8\cdot37\)
=75480
y!=17!
\(M=\frac{A_{y+1}^4+3\cdot C_{y}^3}{y!}=\frac{75480}{17!}=\frac{4440}{16!}=\frac{277.5}{15!}\)
=>Không có câu nào đúng
