If $\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}$,find $x$.

The total number of six-digit numbers formed using the digits $4, 5, 9$ only and divisible by $6$ is $.........$.

Words with or without meaning are to be formed using all the letters of the word $EXAMINATION$. The probability that the letter $M$ appears at the fourth position in any such word is:

Consider the set $A = \{1, 2, 3, \ldots, 30\}$. The number of ways in which one can choose three distinct numbers from $A$ such that the product of the chosen numbers is divisible by $9$ is:

Let $5$-digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed,and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.

All possible words (with or without meaning) are formed by taking at least $2$ letters (all different) from the letters of the word '$CURVE$'. If a word is chosen at random from all the words thus formed,then the probability of getting a $3$-letter word is