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:

The number of ways in which $35$ apples can be distributed among $3$ boys so that each can have any number of apples,is

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to

The number of ways of dividing $52$ cards among four players equally is:

$A$ committee of $4$ persons is to be formed from $2$ ladies,$2$ old men,and $4$ young men such that it includes at least $1$ lady,at least $1$ old man,and at most $2$ young men. The total number of ways in which this committee can be formed is:

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n + 1} - T_n = 21$,then $n$ equals: