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?

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

The number of numbers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) which are multiples of $3$ is?

The sum of the digits in the unit's place of all the $4-$digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is

$^nC_r + 2^nC_{r-1} + ^nC_{r-2} = $