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How many numbers between 99 and 1000 can be formed from the digits 2,3,7,0,8,6 so that in each number each digit may occur once only?
- a)100
- b)90
- c)120
- d)80
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
How many numbers between 99 and 1000 can be formed from the digits 2,3...
Solution:
To find the total number of numbers that can be formed from the given digits, we must first calculate the total number of permutations of the given digits.
Total number of permutations of the given digits = 6P6 = 720
Now, we need to find the number of such permutations that lie between 99 and 1000.
Numbers between 99 and 1000 can be of the form:
1. _ _ _
2. 1 _ _
3. 9 _ _
Case 1:
For the first digit, we have 4 choices (2, 3, 7, 8) as 0 cannot be the first digit.
For the second digit, we have 5 choices (0, 2, 3, 7, 8) as any of the remaining 5 digits can be used.
For the third digit, we have 4 choices (remaining 4 digits) as we cannot repeat any digit.
Total number of permutations in case 1 = 4 × 5 × 4 = 80
Case 2:
For the second and third digits, we have 5 and 4 choices respectively (as explained above).
Total number of permutations in case 2 = 1 × 5 × 4 = 20
Case 3:
For the third digit, we have 3 choices (0, 2, 3) as we cannot use 7, 8, or 6.
Total number of permutations in case 3 = 1 × 1 × 3 = 3
Total number of required permutations = 80 + 20 + 3 = 103
Therefore, the correct option is (A) 100.
To find the total number of numbers that can be formed from the given digits, we must first calculate the total number of permutations of the given digits.
Total number of permutations of the given digits = 6P6 = 720
Now, we need to find the number of such permutations that lie between 99 and 1000.
Numbers between 99 and 1000 can be of the form:
1. _ _ _
2. 1 _ _
3. 9 _ _
Case 1:
For the first digit, we have 4 choices (2, 3, 7, 8) as 0 cannot be the first digit.
For the second digit, we have 5 choices (0, 2, 3, 7, 8) as any of the remaining 5 digits can be used.
For the third digit, we have 4 choices (remaining 4 digits) as we cannot repeat any digit.
Total number of permutations in case 1 = 4 × 5 × 4 = 80
Case 2:
For the second and third digits, we have 5 and 4 choices respectively (as explained above).
Total number of permutations in case 2 = 1 × 5 × 4 = 20
Case 3:
For the third digit, we have 3 choices (0, 2, 3) as we cannot use 7, 8, or 6.
Total number of permutations in case 3 = 1 × 1 × 3 = 3
Total number of required permutations = 80 + 20 + 3 = 103
Therefore, the correct option is (A) 100.
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How many numbers between 99 and 1000 can be formed from the digits 2,3...
All 3 digit no.s lies between 99 and 1000.First place should not be filled with '0'.This can be done in 5 ways...(I) Remaining 2 digits can be filled in 5p2 ways.. (ll) .From (I) and (ll) No. of no.s between 99 and 1000 can be formed from given digits =5*5p2=100.
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How many numbers between 99 and 1000 can be formed from the digits 2,3,7,0,8,6 so that in each number each digit may occur once only?a)100b)90c)120d)80Correct answer is option 'A'. Can you explain this answer?
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