JEE Exam > JEE Questions > Five digit number divisible by 3 is formed us...
Start Learning for Free
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers is
- a)312
- b)3125
- c)120
- d)216
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, ...
Free Test
FREE
| Start Free Test |
Community Answer
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, ...
Approach:
To find the total number of five-digit numbers that are divisible by 3 using the digits 0, 1, 2, 3, 4, and 5 without repetition, we need to follow the below steps:
Step 1: Determine the total number of ways to arrange the digits
- Since we cannot repeat any digit, the total number of ways to arrange the digits is 6P5 = 6! / (6-5)! = 6*5*4*3*2 = 720.
Step 2: Determine the total number of five-digit numbers divisible by 3
- For a number to be divisible by 3, the sum of its digits must be divisible by 3.
- The sum of the given digits {0, 1, 2, 3, 4, 5} is 15, which is divisible by 3.
- There are a total of 5! = 120 ways to arrange the digits such that the sum of the digits is divisible by 3.
Step 3: Calculate the total number of five-digit numbers
- The total number of five-digit numbers that can be formed using the given digits without any restrictions is 6P5 = 720.
Step 4: Calculate the number of five-digit numbers divisible by 3
- The total number of five-digit numbers divisible by 3 = (Number of ways to arrange digits with sum divisible by 3) * (Number of ways to arrange remaining digit)
- Total number = 120 * 6 = 720.
Therefore, the correct answer is option D) 216.
To find the total number of five-digit numbers that are divisible by 3 using the digits 0, 1, 2, 3, 4, and 5 without repetition, we need to follow the below steps:
Step 1: Determine the total number of ways to arrange the digits
- Since we cannot repeat any digit, the total number of ways to arrange the digits is 6P5 = 6! / (6-5)! = 6*5*4*3*2 = 720.
Step 2: Determine the total number of five-digit numbers divisible by 3
- For a number to be divisible by 3, the sum of its digits must be divisible by 3.
- The sum of the given digits {0, 1, 2, 3, 4, 5} is 15, which is divisible by 3.
- There are a total of 5! = 120 ways to arrange the digits such that the sum of the digits is divisible by 3.
Step 3: Calculate the total number of five-digit numbers
- The total number of five-digit numbers that can be formed using the given digits without any restrictions is 6P5 = 720.
Step 4: Calculate the number of five-digit numbers divisible by 3
- The total number of five-digit numbers divisible by 3 = (Number of ways to arrange digits with sum divisible by 3) * (Number of ways to arrange remaining digit)
- Total number = 120 * 6 = 720.
Therefore, the correct answer is option D) 216.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?
Question Description
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?.
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?.
Solutions for Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup