Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

A car manufacturing factory has two plants $$X$$ and $$Y$$. Plant $$X$$ manufactures $$70 \%$$ of cars and plant $$Y$$ manufactures $$30 \%$$ of cars. $$80 \%$$ of cars at plant $$X$$ and $$90 %$$ of cars at plant $$Y$$ are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant $$X$$ is :

In a certain two $$65 \%$$ families own cell phones, 15000 families own scooter and $$15 \%$$ families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

$$A$$ and $$B$$ are non-singleton sets and $$n(A \times B)=35$$. If $$B \subset A$$, then $${ }^{n(A)} C_{n(B)}$$ is equal to