Question

Let $x_1,x_2,...,x_{15}$ be $15$ district numbers chosen from $1,2,3,...,15$. Then the value of $(x_1-1)(x_2-1)(x_3-1)...(x_{15}-1)$ is

• A. always $\le 0$
• B. $0$ (zero)
• C. always even
• D. always odd

Answer 1

The correct option is B $0$ (zero)

Among $x_1,x_2,...,x_{15}$,
one of them, $x_k$ will always be $1$.
$x_k-1=0$
Thus, the given product is zero.