The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $$2,3,4,5,6$$ (repetition of digits is not allowed) and divisible by 55 is _________.

The number of matrices of order $$3 \times 3$$, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is __________.

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $$\mathrm{b}+3 \mathrm{~g}$$ is equal to ____________.

Let $$S$$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $$\{A, B, C, D, E\}$$ or a number from $$\{1,2,3,4,5\}$$ with the repetition of characters allowed. If the number of passwords in $$S$$ whose at least one character is a number from $$\{1,2,3,4,5\}$$ is $$\alpha \times 5^{6}$$, then $$\alpha$$ is equal to ___________.