A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is
$90 \times (\frac{1}{4})^6$
$\frac{45}{2} (\frac{3}{4})^4 $
$90 \times (\frac{1}{2})^{10} $
$(\frac{1}{2})^{10}$
If six students, including two particular students $A$ and $B,$ stand in a row, then the probability that $A$ and $B$ are separated with one student in between them is
Five digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$ and $8$. What is the probability that they have even digits at both the ends
When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is
There are $10$ engineering colleges and five students $A, B, C, D, E$ . Each of these students got offer from all of these $10$ engineering colleges. They randomly choose college independently of each other. Tne 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
Two digits are selected randomly from the set $\{1, 2,3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that minimum of the two digits is less than $5$ is