In a certain examination,a candidate has to pass in each of the $5$ subjects. The number of ways in which the candidate can fail is:

Let $A$ be a set containing $n$ elements. If $P$ and $Q$ are two subsets of $A$, then the number of ways of choosing $P$ and $Q$ such that $P \cap Q = \phi$ is:

Let $A = \{n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of } 3 \text{ nor a multiple of } 4\}$. Then the number of elements in $A$ is

If $P(A^c) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^c) = 0.5$,then find $P[B / (A \cup B)^c]$.

Let $A = \{n \in N : n \text{ is a } 3 \text{-digit number}\}$. Let $B = \{9k + 2 : k \in N\}$ and $C = \{9k + l : k \in N\}$ for some $l$ $(0 < l < 9)$. If the sum of all the elements of the set $A \cap (B \cup C)$ is $274 \times 400$,then $l$ is equal to:

In a group of $65$ people,$40$ like cricket and $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?