In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $A, B$ and $C$. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section $A$ has 8 questions, section $B$ has 6 questions and section $C$ has 6 questions, then the total number of ways a student can select 15 questions is __________.

<p>The problem involves choosing 15 questions out of a total of 20 available questions, with the constraint that at least 4 questions must be chosen from each of the three sections A, B, and C. To evaluate the total number of ways a student can select these questions, we need to consider every possible combination of questions from sections A, B, and C that sum up to 15 questions while respecting the constraints.</p><p>Section A has 8 questions, Section B and C each have 6 questions. The student must choose at least 4 questions from each section, which satisfies the minimum requirement. However, since the student is to attempt a total of 15 questions, there are several combinations to consider, as outlined below:</p><ul><li>Choosing 4 questions from A, 5 from B, and 6 from C</li><li>Choosing 4 questions from A, 6 from B, and 5 from C</li><li>Choosing 7 questions from A, 4 from B, and 4 from C</li><li>Choosing 6 questions from A, 5 from B, and 4 from C</li><li>Choosing 6 questions from A, 4 from B, and 5 from C</li><li>Choosing 5 questions from A, 5 from B, and 5 from C</li><li>Choosing 5 questions from A, 6 from B, and 4 from C</li><li>Choosing 5 questions from A, 4 from B, and 6 from C</li></ul> <br/>$$ \begin{array}{|c|c|c|l|c|} \hline \mathrm{A} & \mathrm{B} & \mathrm{C} & \Rightarrow & \begin{array}{c} \text { No. of } \\ \text { question } \end{array} \\ \hline 4 & 5 & 6 & \rightarrow & { }^8 C_4{ }^6 C_5{ }^6 C_6 \\ \hline 4 & 6 & 5 & \rightarrow & { }^8 C_4{ }^6 C_6{ }^6 C_5 \\ \hline 7 & 4 & 4 & \rightarrow & { }^8 C_7{ }^6 C_4{ }^6 C_4 \\ \hline 6 & 5 & 4 & \rightarrow & { }^8 C_6{ }^6 C_5{ }^6 C_4 \\ \hline 6 & 4 & 5 & \rightarrow & { }^8 C_6{ }^6 C_4{ }^6 C_5 \\ \hline 5 & 5 & 5 & \rightarrow & { }^8 C_5{ }^6 C_5{ }^6 C_5 \\ \hline 5 & 6 & 4 & \rightarrow & { }^8 C_5{ }^6 C_6{ }^6 C_4 \\ \hline 5 & 4 & 6 & \rightarrow & { }^8 C_5{ }^6 C_4{ }^6 C_6 \\ \hline \end{array} $$ <br/><br/>Total ways of select $=11376$