$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

There are $6$ men and $8$ women in a club. $A$ committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if $2$ men and $3$ women are selected?

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 different ways can the letters of the word '$LEADING$' be arranged in such a way that the vowels always come together?

Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is: