The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

Among the $4$-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6$ without repeating any digit,the number of numbers which are divisible by $6$ is:

Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff,if five different flags are available.

The number of ways of distributing $15$ apples to three persons $A, B, C$ such that $A$ and $C$ each get at least $2$ apples and $B$ gets at most $5$ apples is

The value of $\sum \limits_{r=0}^{22} {}^{22}C_{r} \cdot {}^{23}C_{r}$ is $.......$

Number of all possible words (with or without meaning) that can be formed using all the letters of the word $CABINET$ in which neither the word $CAB$ nor the word $NET$ appear is