If a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively is

Two digits are selected randomly from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that the minimum of the two digits is less than $5$ is

There are $10$ engineering colleges and five students $A, B, C, D, E$. Each of these students received an offer from all of these $10$ engineering colleges. They randomly choose a college independently of each other. The probability that all get admission in different colleges can be expressed as $\frac{a}{b}$,where $a$ and $b$ are co-prime numbers. Then the value of $a + b$ is:

If three dice are thrown simultaneously,then the probability of getting a score of $7$ is

Two points are randomly chosen on the circumference of a circle of radius $r$. The probability that the distance between the two points is at least $r$ is equal to

From a pack of $52$ playing cards,three cards are drawn simultaneously. The probability that these are one king,one queen,and one jack is: