# 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. - Mathematics

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?

#### 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 =${}^5 C_3 \times^7 C_5 + {}^5 C_4 \times^7 C_4 +^5 C_5 \times^7 C_3 = 210 + 175 + 35 = 420$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 31 | Page 17