There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them equals

The total number of words that can be formed using the letters $a, b, c, d, e, f$ taken $3$ at a time such that each word contains at least one vowel is:

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

If $(n+1)! = 6[(n-1)!]$,find $n$.

Let $n > 2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track. Further,each pair of nearest stations is connected by a blue line,whereas all remaining pairs of stations are connected by a red line. If the number of red lines is $99$ times the number of blue lines,then the value of $n$ is

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls are: