Permutation Combination Question 6
Question 6 - 2024 (30 Jan Shift 2)
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
Show Answer
Answer (11376)
Solution
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 $={ }^{8} c _5 \cdot{ }^{6} c _5 \cdot{ }^{6} c _5+{ }^{8} c _6{ }^{6} c _5 \cdot{ }^{6} c _4 \times 2+$
${ }^{8} c _5 \cdot{ }^{6} c _6 \cdot{ }^{6} c _4 \times 2+{ }^{8} c _4 \cdot{ }^{6} c _6 \cdot{ }^{6} c _5 \times 2+{ }^{8} c _7 \cdot{ }^{6} c _4 \cdot{ }^{6} c _4$
$=56 \cdot 6 \cdot 6+28 \cdot 6 \cdot 15 \cdot 2+56 \cdot 15 \cdot 2+70 \cdot 6 \cdot 2$
$+8 \cdot 15 \cdot 15$
$=2016+5040+1680+840+1800=11376$
