If three unbiased dice are rolled simultaneously, then the probability that all the three dice show distinct numbers is

Three persons $A, B$ and $C$ attended a recruitment test, The ratio of the chances of $A, B, C$ in getting through the test is $1: 2: 3$ and their probabilities to face the interview successfully are $0.8,0.7,0.6$, respectively. If one of them is to be selected for the post, then the probability that $A$ gets the post is

Two cards are drawn at random one after the other with replacement from a pack of 52 playing cards. Then, the variance of the random variable of the number of spade cards among the drawn cards is

Let $A=(2,0)$ and $B=(0,-2)$. Let $P$ be any point such that the sum of the distance of $P$ from $A$ and $B$ is 4 . Then, the equation of the locus of the point $P$ is