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How many numbers between 3000 and 4000 divisible by 5 can be formed from the digits 3,4,5,6,7,8 if repetition of any digit is not allowed?
- a)60
- b)12
- c)120
- d)24
Correct answer is option 'B'. Can you explain this answer?
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How many numbers between 3000 and 4000 divisible by 5 can be formed fr...
To find the number of numbers between 3000 and 4000 that are divisible by 5 using the digits 3, 4, 5, 6, 7, and 8 without repetition of digits, we can follow these steps:
Step 1: Determine the possible choices for the thousands place
Since the number has to be between 3000 and 4000, the thousands place can only be filled with the digit 3. So, there is only 1 choice for the thousands place.
Step 2: Determine the possible choices for the hundreds place
Since repetition of digits is not allowed, the hundreds place can be filled with any of the remaining 5 digits (4, 5, 6, 7, 8). So, there are 5 choices for the hundreds place.
Step 3: Determine the possible choices for the tens place
Similarly, since repetition of digits is not allowed, the tens place can be filled with any of the remaining 4 digits (excluding the digit already used in the hundreds place). So, there are 4 choices for the tens place.
Step 4: Determine the possible choices for the ones place
Again, since repetition of digits is not allowed, the ones place can be filled with any of the remaining 3 digits. So, there are 3 choices for the ones place.
Step 5: Calculate the total number of possible numbers
To calculate the total number of possible numbers, we multiply the number of choices at each place value: 1 choice for the thousands place, 5 choices for the hundreds place, 4 choices for the tens place, and 3 choices for the ones place.
Total number of possible numbers = 1 * 5 * 4 * 3 = 60
Therefore, the correct answer is option B) 12
Step 1: Determine the possible choices for the thousands place
Since the number has to be between 3000 and 4000, the thousands place can only be filled with the digit 3. So, there is only 1 choice for the thousands place.
Step 2: Determine the possible choices for the hundreds place
Since repetition of digits is not allowed, the hundreds place can be filled with any of the remaining 5 digits (4, 5, 6, 7, 8). So, there are 5 choices for the hundreds place.
Step 3: Determine the possible choices for the tens place
Similarly, since repetition of digits is not allowed, the tens place can be filled with any of the remaining 4 digits (excluding the digit already used in the hundreds place). So, there are 4 choices for the tens place.
Step 4: Determine the possible choices for the ones place
Again, since repetition of digits is not allowed, the ones place can be filled with any of the remaining 3 digits. So, there are 3 choices for the ones place.
Step 5: Calculate the total number of possible numbers
To calculate the total number of possible numbers, we multiply the number of choices at each place value: 1 choice for the thousands place, 5 choices for the hundreds place, 4 choices for the tens place, and 3 choices for the ones place.
Total number of possible numbers = 1 * 5 * 4 * 3 = 60
Therefore, the correct answer is option B) 12
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Community Answer
How many numbers between 3000 and 4000 divisible by 5 can be formed fr...
The no. is divisible by 5 iff it's unit digit is 0 or 5 but we have only 5 so for unit digit 1 way.
the no. is in b/w 3000&4000 so the no. start with 3 as 1 way
now we have 4 more digit which will be put in 4 and 3 ways to avoid repitition.
total no.is 1×4×3×1=12
the no. is in b/w 3000&4000 so the no. start with 3 as 1 way
now we have 4 more digit which will be put in 4 and 3 ways to avoid repitition.
total no.is 1×4×3×1=12
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How many numbers between 3000 and 4000 divisible by 5 can be formed from the digits 3,4,5,6,7,8 if repetition of any digit is not allowed?a)60b)12c)120d)24Correct answer is option 'B'. Can you explain this answer?
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