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In an examination, a question pater cons...

In an examination, a question pater 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 students select the questions ?

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selection for I & II
when 3,5 selected `.^5C_3.^7C_5`
when 4, 4 selected `.^5C_4.^7C_4`
when 5,3 slected `.^5C_5.^7C_3`
required = `(5!)/(3!2!) * (7!)/(5!2!) + (5!)/(4!1!)*(7!)/(4!3!) + (5!)/(5!0!)*(7!)/(3!4!)`
= `7*6*5 + 5*7*5 + 7*5`
`= 210 + 175 + 35`
`= 210+210 = 420`
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