If `a` denotes the number of permutations of `(x+2)` things taken all at a time, `b` the number of permutations of `x` things taken `11` at a time and `c` the number of permutations of `x-11` things taken all at a time such that `a=182b c ,` find the value of `xdot`

Explanation

To solve the problem, we need to find the value of \( x \) given the relationship between permutations \( a \), \( b \), and \( c \). Let's break down the steps:

### Step 1: Define the permutations
- \( a \) is the number of permutations of \( (x + 2) \) things taken all at a time:
\[ a = P(x + 2, x + 2) = (x + 2)! \]

...