Question

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 _______.

Answer 1

Correct answer: 11376

If 4 questions from each section are selected

Remaining 3 questions can be selected either in \((1, 1,1)\) or \((3,0,0)\) or \((2,1,0)\)

\(\therefore\) Total ways \(={ }^{8} \mathrm{c}_{5} \cdot{ }^{6} \mathrm{c}_{5} \cdot{ }^{6} \mathrm{c}_{5}+{ }^{8} \mathrm{c}_{6}{ }^{6} \mathrm{c}_{5} \cdot{ }^{6} \mathrm{c}_{4} \times 2+{ }^{8} \mathrm{c}_{5} \cdot{ }^{6} \mathrm{c}_{6} \cdot{ }^{6} \mathrm{c}_{4} \times 2+{ }^{8} \mathrm{c}_{4} \cdot{ }^{6} \mathrm{c}_{6} \cdot{ }^{6} \mathrm{c}_{5} \times 2+{ }^{8} \mathrm{c}_{7} \cdot{ }^{6} \mathrm{c}_{4} \cdot{ }^{6} \mathrm{c}_{4}\)

\(=56.6 .6+28.6 .15 .2+56.15 .2+70.6 .2+8.15 .15\)

\(=2016+5040+1680+840+1800\)

\(=11376\)