$\frac{4}{15}$of $\frac{5}{7}$ of a number is greater than $\frac{4}{9}$ of $\frac{2}{5}$ of the same number by $8$. What is half of that number?

How many times is number '3' preceded by number '7' and not followed by an even number?

How many such $4^{\prime }s$ are there in the given below arrangement which are immediately preceded by a pair of numbers whose product is more than the product of a pair of numbers immediately following $4$?

$4378445643241744521468948947864254462$