Question

The value of the determinant $\left|\begin{array}{ccc}{}^5{C}_0& {}^5{C}_3& 14\\ {}^5{C}_1& {}^5{C}_4& 1\\ {}^5{C}_2& {}^5{C}_5& 1\end{array}\right|$ is

• A. $0$
• B. $-576$
• C. $80$
• D. none of these

Answer 1

The correct option is B $-576$

$\left|\begin{array}{ccc}{}^5{C}_0& {}^5{C}_3& 14\\ {}^5{C}_1& {}^5{C}_4& 1\\ {}^5{C}_2& {}^5{C}_5& 1\end{array}\right|=\left|\begin{array}{ccc}1& 10& 14\\ 5& 5& 1\\ 10& 1& 1\end{array}\right|$

$=1(5-1)-10(5-10)+14(5-50)$

$=4+50-630=-576$