A five-digits number is formed by using the digits $$1,2,3,4,5$$ with no repetition. The probability that the numbers 1 and 5 are always together, is

If a number $n$ is chosen at random from the set $$\{11,12,13, \ldots \ldots, 30\}$$. Then, the probability that $$n$$ is neither divisible by 3 nor divisible by 5, is

Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form the vertices of an isosceles triangle, is

If $$A, B$$ and $$C$$ are mutually exclusive and exhaustive events of a random experiment such that $$P(B)=\frac{3}{2} P(A)$$ and $$P(C)=\frac{1}{2} P(B)$$, then $$P(A \cup C)$$ equals to