Let

$\mathrm{A}=\{(a, b, c): a, b, c$ are non-negative integers and $a+b+2 c=22\}$.

Then $n(\mathrm{~A})$ is equal to :

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon.
If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is :

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is: