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Total number of natural numbers less than 4000 formed with digits 0,1,2,3,4,5 and 8 is :
- a)647
- b)1295
- c)370
- d)none
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Total number of natural numbers less than 4000 formed with digits 0,1,...
The one digit number will be 6
The 2 digit number will be
6 x 7 = 42
The 3 digit number will be
6 x 7 x 7 = 294
The 4 digit unit number will be
3 x 7 x 7 x 7 = 1029
so total number from 0 to 4000 excluding 4000 will be
6 + 42 + 294+ 1029= 1371
The 2 digit number will be
6 x 7 = 42
The 3 digit number will be
6 x 7 x 7 = 294
The 4 digit unit number will be
3 x 7 x 7 x 7 = 1029
so total number from 0 to 4000 excluding 4000 will be
6 + 42 + 294+ 1029= 1371
Most Upvoted Answer
Total number of natural numbers less than 4000 formed with digits 0,1,...
Total number of natural numbers less than 4000 formed with digits 0, 1, 2, 3, 4, 5, and 8 can be found by considering the following cases:
1. Numbers with 1 digit:
- We can choose any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 7 numbers with 1 digit.
2. Numbers with 2 digits:
- The first digit can be any digit from 1, 2, 3, 4, 5, and 8, so there are 6 choices.
- The second digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 6 * 7 = 42 numbers with 2 digits.
3. Numbers with 3 digits:
- The first digit can be any digit from 1, 2, 3, 4, 5, and 8, so there are 6 choices.
- The second digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- The third digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 6 * 7 * 7 = 294 numbers with 3 digits.
4. Numbers with 4 digits:
- The first digit can be any digit from 1, 2, 3, 4, 5, and 8, so there are 6 choices.
- The second digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- The third digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- The fourth digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 6 * 7 * 7 * 7 = 2058 numbers with 4 digits.
Adding up the numbers from each case:
7 + 42 + 294 + 2058 = 2401
Therefore, the total number of natural numbers less than 4000 formed with digits 0, 1, 2, 3, 4, 5, and 8 is 2401.
Hence, the correct answer is option D) none.
1. Numbers with 1 digit:
- We can choose any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 7 numbers with 1 digit.
2. Numbers with 2 digits:
- The first digit can be any digit from 1, 2, 3, 4, 5, and 8, so there are 6 choices.
- The second digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 6 * 7 = 42 numbers with 2 digits.
3. Numbers with 3 digits:
- The first digit can be any digit from 1, 2, 3, 4, 5, and 8, so there are 6 choices.
- The second digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- The third digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 6 * 7 * 7 = 294 numbers with 3 digits.
4. Numbers with 4 digits:
- The first digit can be any digit from 1, 2, 3, 4, 5, and 8, so there are 6 choices.
- The second digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- The third digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- The fourth digit can be any digit from 0, 1, 2, 3, 4, 5, and 8, so there are 7 choices.
- Therefore, there are 6 * 7 * 7 * 7 = 2058 numbers with 4 digits.
Adding up the numbers from each case:
7 + 42 + 294 + 2058 = 2401
Therefore, the total number of natural numbers less than 4000 formed with digits 0, 1, 2, 3, 4, 5, and 8 is 2401.
Hence, the correct answer is option D) none.
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Total number of natural numbers less than 4000 formed with digits 0,1,2,3,4,5 and 8 is :a)647b)1295c)370d)noneCorrect answer is option 'D'. Can you explain this answer?
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