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In an examination, a student has to answer 4 questions out of 5 questions, questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
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Verified Answer
Since a student has to answer 4 questions out of 5 questions \& out of which 2 questions are compulsory. Therefore, we have to choose $(4-2)$ or 2 questions out of $(5-2)$ or 3 questions.
$\therefore$ Total number of ways
$$
={ }^{5-2} C_{4-2}={ }^3 C_2=\frac{3 !}{2 ! 1 !}=\frac{3 \times 2 !}{2 !}=3 .
$$
$\therefore$ Total number of ways
$$
={ }^{5-2} C_{4-2}={ }^3 C_2=\frac{3 !}{2 ! 1 !}=\frac{3 \times 2 !}{2 !}=3 .
$$
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