The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ such that at least two digits are identical is

There are $5$ students in class $10$,$6$ students in class $11$,and $8$ students in class $12$. If the number of ways,in which $10$ students can be selected from them so as to include at least $2$ students from each class and at most $5$ students from the total $11$ students of class $10$ and $11$ is $100k$,then $k$ is equal to $......$

The number of four-lettered words that can be formed from the letters of the word $MAYANK$ such that both $A$'s are included but never together,is equal to:

There are three sections in a question paper,each containing $4$ questions. If a candidate has to answer only $5$ questions from this paper without leaving any section,then the number of ways the candidate can make the choice of questions is:

If the letters of the word $INTERMEDIATE$ are arranged,what is the probability that the two $E$'s do not come together?

$A$ linguistic club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group including the selection of a leader (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is