Question

If $\left|\begin{array}{cccc}x& 4& 7& 9\\ 0& 1& 5& 8\\ 0& 0& 2& 6\\ 0& 0& 0& 3\end{array}\right|=$ the total number of arrangements of $4$ different things, takings at least one at a time, then $x$ is equal to

• A. $\frac{11}{8}$
• B. $4$
• C. $\frac{11}{2}$
• D. $\frac{32}{3}$

Answer 1

The correct option is D $\frac{32}{3}$

$\left|\begin{array}{cccc}x& 4& 7& 9\\ 0& 1& 5& 8\\ 0& 0& 2& 6\\ 0& 0& 0& 3\end{array}\right|{=}^4{P}_1{+}^4{P}_2{+}^4{P}_3{+}^4{P}_4$
$x\left|\begin{array}{ccc}1& 5& 8\\ 0& 2& 6\\ 0& 0& 3\end{array}\right|=4+12+24+24$
$\Rightarrow x\left(6\right)=64$

$\Rightarrow x=\frac{32}{3}$