How is this product of terms calculated?

[crv357]

$\prod_{j \neq i}^{6} (\lambda_{i}-\lambda_{j})$

 

[Mark44]

$\prod_{j \neq i}^{6} \frac{\lambda_{i}}{\lambda_{i}-\lambda_{j}}$

We require you to at least show your thoughts. To help you get started, there are 36 different pairs (i , j) pairs where i and j range between 1 and 6. Some of these pairs aren't going to be allowed in the product above. So how many factors will there be in the product?

 

[member 587159]

The index sign $j \neq i$ means that you take the product over all pairs $(j,i)$ in the set $\{(j,i): 1\leq j,i \leq 6, i \neq j\}$. For example $(1,2)$ and $(2,1)$ are elements of this set, but $(1,1)$ is not.