If 5 letters are to be placed in 5 -addressed envelopes, then the probability that atleast one letter is placed in the wrongly addressed envelope, is

A student writes an examination which contains eight true of false questions. If he answers six or more questions correctly, the passes the examination. If the student answers all the questions, then the probability that he fails in the examination, is

The probabilities that a person goes to college by car is $\frac{1}{5}$, by bus is $\frac{2}{5}$ and by train is $\frac{3}{5}$, respectively. The probabilities that he reaches the college late if he takes car, bus and train are $\frac{2}{7}, \frac{4}{7}$ and $\frac{1}{7}$, respectively, If he reaches the college on time, then probability that he travelled by car is

$P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2}{3}, \frac{3}{5}, \frac{5}{7}$ respectively, then the probability that the target is his by $P$ or $Q$ but not by $R$ is