The probability that at least one of the events $E_1$ and $E_2$ occurs is $0.6$. If the probability of the simultaneous occurrence of $E_1$ and $E_2$ is $0.2$,then $P(E_1') + P(E_2') = $

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 class of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. Then the number of newspapers is

Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey. $24$ played all three games. The number of boys who did not play any game is:

If sets $A$ and $B$ have $3$ and $6$ elements respectively,what is the minimum number of elements in $A \cup B$?

Let $\bigcup_{i=1}^{50} X_{i} = \bigcup_{i=1}^{n} Y_{i} = T$,where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of the sets $X_{i}$ and exactly $6$ of the sets $Y_{i}$,then $n$ is equal to: