The Number of Finishers at a Particularly Difficult Race Is $$f ( x ) = \left\{ \begin{array} { l l } \frac { 36 } { 35 ( x ) ( x + 1 ) } & x = 1 , \ldots , 35 \\0 & \text { else. }\end{array} \right.$$

Short Answer

The number of finishers at a particularly difficult race is a random variable with probability mass function: $$f ( x ) = \left\{ \begin{array} { l l } \frac { 36 } { 35 ( x ) ( x + 1 ) } & x = 1 , \ldots , 35 \\0 & \text { else. }\end{array} \right.$$ Find the probability that at least 3 people do not finish.