Is the language in the description context free? I am stuck on a question. Lets say there is a string that can be created from three alphabets a,b,c the condition is number of a&lt;= number of b&lt;= number of c. I can solve if there are a and b (two alphabets) but I am not able to solve for 3. Any help will be appreciated.
Thanks
The basic problem here is that context-free languages are not closed under intersection. 

The example you give illustrates this. Thus, $\{ w\in\{a,b,c\}^* \mid |w|_a \le |w|_b\}$ is context-free, and similarly, so is $\{ w\in\{a,b,c\}^* \mid |w|_b \le |w|_c\}$. The intersection of these two languages $\{ w\in\{a,b,c\}^* \mid |w|_a \le |w|_b \le |w|_c\}$ is not context-free.