The total number of ways of selecting six coins out of $20$ one-rupee coins,$10$ fifty-paise coins,and $7$ twenty-five-paise coins is:

$A$ question paper has $2$ parts,part $A$ and part $B$,each containing $10$ questions. If a student has to choose $8$ questions from part $A$ and $5$ questions from part $B$,in how many ways can the student choose the questions?

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

$A$ committee of $5$ members is to be formed out of $3$ trainees,$4$ professors,and $6$ research associates. In how many different ways can this be done if the committee should have all $4$ professors and $1$ research associate $OR$ all $3$ trainees and $2$ professors?

How many $5$-digit even numbers can be formed using the digits $1, 2, 5, 5, 4$?

$A$ person goes in for an examination in which there are four papers with a maximum of $m$ marks from each paper. The number of ways in which one can get $2m$ marks is