$A$ group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least one boy and one girl?

Two players $A$ and $B$ play a series of games of badminton. The player,who wins $5$ games first,wins the series. Assuming that no game ends in a draw,the number of ways,in which player $A$ wins the series is . . . . . . .

Six '$+$' and four '$-$' signs are to be placed in a straight line so that no two '$-$' signs come together. Then the total number of ways is:

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

The number of values of $n \in N$ for which ${ }^{n+2} C_2 : { }^{n+3} C_1 = 4 : 2$ is

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