The number of ways in which ten candidates $A_1, A_2, ....... A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is

The value of ${2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 3) \cdot (2n - 1) \}$ is

The number of words that can be formed using the letters of the word $ARTICLE$,such that the vowels occupy even places,is

The number of ways in which any four letters can be selected from the word $CORGOO$ is

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

Consider three boxes,each containing $10$ balls labelled $1, 2, dots, 10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$ the label of the ball drawn from the $i^{th}$ box,$(i = 1, 2, 3)$. Then,the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is: