How many $3$-digit numbers,each less than $600$,can be formed from the digits $1, 2, 3, 4, 5,$ and $9$,if repetition of digits is allowed?

In how many ways can $15$ different books be divided equally among $5$ sets or groups?

There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is:

$A$ lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends,if two of the friends will not attend the party together is

How many numbers of five digits can be formed with the digits $0, 1, 2, 3, 5$ and $6$?

$A$ 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?