Permutations And Combinations Question 327

Question: Find the number of integral solution of the equation $ x+y+z=20 $ and $ x>-1,y>-2 $ and $ z>-3. $

Options:

A) $ ^{25}C _{23} $

B) $ ^{17}C_2 $

C) $ ^{23}C_2 $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a] Since as per the given condition $ x>-1, $ so x is non-negative integer, $ y>-2soy=-1+b $ and similarly $ z>3soz=-2+c $ or $ (x)+(-1+b)+(-2+c)=23 $ or $ x+b+c=23 $ And we need to find the number of non-negative integral solution of the equation $ x+b+c=23 $ which is, $ ^{23+3-1}{C _{3-1}}{{=}^{25}}C_2{{=}^{25}}C _{23} $

Engineering Preparation

Physics 11th

Physics 12th

Chemistry 11th

Chemistry 12th

Mathematics 11th

Mathematics 12th

JEE Previous Year Questions

JEE Tutorial Sessions

Medical Preparation

Physics 11th

Physics 12th

Chemistry 11th

Chemistry 12th

Biology 11th

Biology 12th

NEET Previous Year Questions

NEET Tutorial Sessions

NCERT Books & Solutions

NCERT Books for JEE

NCERT Books for NEET

NCERT Solutions for JEE

NCERT Solutions for NEET

NCERT Exemplar for JEE

NCERT Exemplar for NEET

Important Resources

Physics Formulas

Chemistry Formulas

Mathematics Formulas

JEE Articles

NEET Articles

Other Resources

Media Coverage

Help Videos

Current Affair

Student Help Booklet

SPOC Help Booklet

SATHEE Forum

Syllabus

JEE Syllabus

NEET Syllabus

Mentorship

Mentorship for JEE

Mentorship for NEET

NCERT Exemplar Video Solutions

NCERT Exercise Video Solution

JEE Chemistry

Organic Chemistry PYQ

JEE PYQ Chapterwise

JEE Chemistry Organic Chemistry

pyqs

Medical Scholarships

Medical Accommodation

Medical Careers

International Students

NRI/OCI Students

JEE Advanced Multi-Correct

JEE Advanced Integer Type

JEE Advanced Paragraph

JEE Advanced Matrix Match

JEE Advanced Reasoning

JEE Advanced Comprehension

JEE Advanced Numerical Answer

JEE Advanced Difficulty Analysis

JEE Advanced Topic Weightage

JEE Advanced Paper Comparison

JEE Advanced Success Strategies

JEE Advanced Preparation Timeline

JEE Advanced Subject Mastery

resources

NEET Biology Strategy

Student Webinars

Counselling Guides

Doubt Clearing

Bridge Programs

revision-hub

Mindmaps Index

success-stories

60% to 99% JEE Journey

NEET 720 Strategy

icon  BETA

© 2014-2025 Copyright SATHEE

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in
Media coverage of SATHEE
goolge

Play Store
goolge

App Store
The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.