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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?
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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.
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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?
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