Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :
Solution
Each section has 5 questions. Candidate must choose 5 questions with at least 1 from each section.Possible distributions among 3 sections (sum = 5, min 1 each):
\[(1,1,3) \quad \text{and} \quad (1,2,2)\]
Case 1 — Distribution (1, 1, 3):
\[\binom{5}{1}\binom{5}{1}\binom{5}{3} = 5 \times 5 \times 10 = 250\]
This arrangement can be done in \(\dfrac{3!}{2!} = 3\) ways, so:
\[250 \times 3 = 750\]
Case 2 — Distribution (1, 2, 2):
\[\binom{5}{1}\binom{5}{2}\binom{5}{2} = 5 \times 10 \times 10 = 500\]
This arrangement can be done in \(\dfrac{3!}{2!} = 3\) ways, so:
\[500 \times 3 = 1500\]
Total number of ways:
\[750 + 1500 = \boxed{2250}\]
✅ Answer = Option (a) 2250
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
