There are $4$ oranges,$5$ apples,and $7$ mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is

In how many ways can a group of $7$ persons be formed from $6$ boys and $4$ girls such that the boys are in the majority?

In how many ways can two balls of the same color be selected from $4$ distinct black balls and $3$ distinct white balls?

At an election,a voter may vote for any number of candidates not exceeding the number to be elected. If $4$ candidates are to be elected out of the $12$ contested in the election and a voter votes for at least one candidate,then the number of ways in which a voter can vote is:

Statement-$1:$ The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3$.
Statement-$2:$ The number of ways of choosing any $3$ places from $9$ different places is $^9C_3$.

Sangeeta plans a dinner party for $6$ guests. Out of $10$ friends,in how many ways can she choose the guests if two specific friends cannot attend the party together?