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

In how many ways can $10$ balls be divided between two boys,if one receives two balls and the other receives eight balls?

The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is