Let $A$ denote the set of all $2$-digit numbers in base $10$ that are equal to four times the sum of the factorials of their digits. The sum of the numbers in $A$ is

If $A$ and $B$ are events of a random experiment with $P(A) = 0.5$,$P(B) = 0.4$ and $P(A \cap B) = 0.3$,then the probability that neither $A$ nor $B$ occurs is

Let $A, B, C$ be three non-void subsets of set $S$. Let $(A \cap C) \cup (B \cap C^{\prime}) = \phi$,where $C^{\prime}$ denotes the complement of set $C$ in $S$. Then:

In a group of $400$ people,$250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

In a survey of $400$ students in a school,$100$ were listed as taking apple juice,$150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

If $P(A) = 0.5$,$P(B) = 0.7$,and $P(A \cap B) = 0.6$,then $P(A \cup B) = \dots$