Academic session 2026-27, Chapter 6 in the current curriculum.
Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter Permutations & Combinations. This page offers a step-by-step solution to the specific question from Exercise 1, Question 4:
How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
. With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
It is given that the 5-digit telephone numbers always start with 67.
Therefore, there will be as many phone numbers as there are ways of filling 3 vacant places
| 6 | 7 |
by the digits 0 – 9, keeping in mind that the digits cannot be repeated.
The units place can be filled by any of the digits from 0 – 9, except digits 6 and 7. Therefore, the units place can be filled in 8 different ways following which, the tens place can be filled in by any of the remaining 7 digits in 7 different ways, and the hundreds place can be filled in by any of the remaining 6 digits in 6 different ways.
Therefore, by multiplication principle, the required number of ways in which 5-digit telephone numbers can be constructed is 8 × 7 × 6 = 336
NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:
Stay updated with our latest educational content and study tips
It’s not about starting over if you took a break to care for children, take care of yourself, be healthy or for any other reason. This is a realistic strategy for the recovery of skills, selection of the right job, and overcoming the resume problem. One year, three years or 10 years of a career … Read more
Read MoreThere’s no need to score 95% or achieve a JEE/NEET rank. You don’t need to score 95% or rank in JEE/NEET to build a solid career. A candid and pragmatic guide to the routes that actually work for students who have an average mark and what to do when faced with the options. If … Read more
Read MoreAI tools, online platforms that are much cheaper than coaching centres and the changing idea of what “structure” even means have upended this argument more in the past two years than in the decade preceding it. Here’s what is really the case for 2026 – and what has actually stayed the same. If you look … Read more
Read MoreStarting to make a new career after 30 isn’t a start from scratch. Marketing, teaching, financial, retail, healthcare, sales and other professionals can pursue careers in technology by applying the existing knowledge and skills they have acquired to new technology skills. There are various ways to enter the technology industry, such as in IT support, … Read more
Read MoreCalculate percentage from obtained marks and total marks.
Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 4: How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number s....
Fresh educational articles and updates.
Most-read articles from SaralStudy.
Fast access to frequently used study resources.
Recently viewed articles based on SaralStudy activity.
Comments
Thank u Very much sir
Thanks sir