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

The number of $4$-digit numbers which are neither a multiple of $7$ nor a multiple of $3$ is ..... .

Let $S = \{p_1, p_2, \ldots, p_{10}\}$ be the set of the first ten prime numbers. Let $A = S \cup P$,where $P$ is the set of all possible products of distinct elements of $S$. Then the number of all ordered pairs $(x, y)$,where $x \in S$ and $y \in A$,such that $x$ divides $y$,is . . . . . .

If $A$ and $B$ are subsets of universal set $X$ such that $n(X)=200, n(A)=90, n(B)=80$ and $n(A' \cap B')=40$,then $n(A \cap B')=$

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:

In a survey of $60$ people,it was found that $25$ people read newspaper $H$,$26$ read newspaper $T$,$26$ read newspaper $I$,$9$ read both $H$ and $I$,$11$ read both $H$ and $T$,$8$ read both $T$ and $I$,and $3$ read all three newspapers. Find the number of people who read exactly one newspaper.