In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

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#### Solution

A question paper consists of 12 questions divided into 2 parts, one with 5 and the other with 7 questions.

A student has to attempt 8 questions out of the 12 questions by selecting at least 3 from each part.

∴ Required number of ways =\[{}^5 C_3 \times^7 C_5 + {}^5 C_4 \times^7 C_4 +^5 C_5 \times^7 C_3 = 210 + 175 + 35 = 420\]

Concept: Concept of Combinations

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