How many numbers of $6$ digits can be formed from the digits of the number $112233$

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is

Let $A_1,A_2,........A_{11}$ are players in a team with their T-shirts numbered $1,2,.....11$. Hundred gold coins were won by the team in the final match of the series. These coins is to be distributed among the players such that each player gets atleast one coin more than the number on his T-shirt but captain and vice captain get atleast $5$ and $3$ coins respectively more than the number on their respective T-shirts, then in how many different ways these coins can be distributed ?

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

How many chords can be drawn through $21$ points on a circle?

The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is