The number of positive integers less than $10000$ which contain the digit $5$ at least once is

The number of seven-digit positive integers formed using the digits $1, 2, 3,$ and $4$ only,such that the sum of the digits is equal to $12$,is $...........$.

$A$ question paper is divided into two parts $A$ and $B$,and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions,selecting at least two questions from each part,is:

How many six-digit numbers are there in which no digit is repeated,even digits appear at even places,odd digits appear at odd places,and the number is divisible by $4$?

Let $n_1 < n_2 < n_3 < n_4 < n_5$ be positive integers such that $n_1+n_2+n_3+n_4+n_5=20$. Then the number of such distinct arrangements $(n_1, n_2, n_3, n_4, n_5)$ is

Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$. Then,the number of ways of choosing $x$ and $y$ such that $x + y$ is divisible by $5$ is $.........$.