If set $A$ contains $8$ elements,then the number of subsets of $A$ which contain at least $6$ elements is

In how many ways can $10$ people be seated in $2$ boats such that each boat has $5$ people and two specific people do not sit in the same boat?

In a shop,there are $5$ types of ice-creams available. $A$ child buys $6$ ice-creams.
$Statement-1$: The number of different ways the child can buy the $6$ ice-creams is $^{10}C_5$.
$Statement-2$: The number of different ways the child can buy the $6$ ice-creams is equal to the number of different ways of arranging $6$ $A$'s and $4$ $B$'s in a row.

There are $15$ people at a party and each person shakes hands with every other person. What is the total number of handshakes?

In an election,there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples,is