There are $15$ persons in a party and each person shakes hands with every other person exactly once. What is the total number of handshakes?

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

The sum of the digits in the unit place of all numbers formed with the help of $3, 4, 5, 6$ taken all at a time is

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

If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is: