NCERT Class XI Mathematics - Permutations and Combinations - Solutions
© examsnet.com
Question : 37
Total: 41
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:
Since at least 3 questions are required to attempt from each part.
Therefore a student can attempt
(a) 3 questions from part I & 5 questions from part II
(b) 4 questions from part I & 4 questions from part II
(c) 5 questions from part I & 3 questions from part II
In case (a), selection can be made in
C 3 ×
C 5
In case (b), selection can be made in
C 4 ×
C 4
In case (c), selection can be made in
C 5 ×
C 3
∴ The required no. of ways =
C 3 ×
C 5 +
C 4 ×
C 4
C 5 ×
C 3
×
×
×
=
×
Therefore a student can attempt
(a) 3 questions from part I & 5 questions from part II
(b) 4 questions from part I & 4 questions from part II
(c) 5 questions from part I & 3 questions from part II
In case (a), selection can be made in
In case (b), selection can be made in
In case (c), selection can be made in
∴ The required no. of ways =
=
© examsnet.com
Go to Question: