The number of $6$-letter words,with or without meaning,that can be formed using the letters of the word $\text{MATHS}$ such that any letter that appears in the word must appear at least twice,is $...$

The number of $6$-digit numbers that can be formed using the digits $0, 1, 2, 5, 7,$ and $9$ which are divisible by $11$,where no digit is repeated,is:

Let $a_1, a_2, \ldots, a_n$ be $n$ non-zero real numbers,of which $p$ are positive and the remaining are negative. The number of ordered pairs $(j, k)$ with $j < k$ for which $a_j a_k$ is positive is $55$. Similarly,the number of ordered pairs $(j, k)$ with $j < k$ for which $a_j a_k$ is negative is $50$. Then,the value of $p^2 + (n-p)^2$ is

If four letters are chosen from the letters of the word $ASSIGNMENT$ and are arranged in all possible ways to form $4$-letter words (with or without meaning),then the total number of such words that can be formed is:

The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball is

Out of all possible $8$-digit numbers formed using all the digits $0, 0, 1, 1, 2, 3, 4, 4$,a number is randomly selected. The probability that the selected number is odd is: