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How many numbers between 200 and 1200 can be formed with the digits 0, 1, 2, 3 (repetition of digits not allowed?
- a)6
- b)18
- c)2
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
How many numbers between 200 and 1200 can be formed with the digits 0,...
The numbers between 200 and 1200 can be formed in the following ways:
1) Numbers with 3 digits: The hundreds place can be filled with 2 or 3, so there are 2 ways. The tens place can be filled with any of the remaining 3 digits, so there are 3 ways. The units place can be filled with any of the remaining 2 digits, so there are 2 ways. Therefore, there are 2*3*2 = 12 such numbers.
2) Numbers with 4 digits: The thousands place can only be filled with 1, so there is 1 way. The hundreds place can be filled with any of the remaining 3 digits (not including 0), so there are 3 ways. The tens place can be filled with any of the remaining 2 digits, so there are 2 ways. The units place can be filled with the remaining 1 digit, so there is 1 way. Therefore, there are 1*3*2*1 = 6 such numbers.
Therefore, a total of 12 + 6 = 18 numbers between 200 and 1200 can be formed with the digits 0, 1, 2, 3 with no repetition of digits. So, option 2 is correct.
1) Numbers with 3 digits: The hundreds place can be filled with 2 or 3, so there are 2 ways. The tens place can be filled with any of the remaining 3 digits, so there are 3 ways. The units place can be filled with any of the remaining 2 digits, so there are 2 ways. Therefore, there are 2*3*2 = 12 such numbers.
2) Numbers with 4 digits: The thousands place can only be filled with 1, so there is 1 way. The hundreds place can be filled with any of the remaining 3 digits (not including 0), so there are 3 ways. The tens place can be filled with any of the remaining 2 digits, so there are 2 ways. The units place can be filled with the remaining 1 digit, so there is 1 way. Therefore, there are 1*3*2*1 = 6 such numbers.
Therefore, a total of 12 + 6 = 18 numbers between 200 and 1200 can be formed with the digits 0, 1, 2, 3 with no repetition of digits. So, option 2 is correct.
Most Upvoted Answer
How many numbers between 200 and 1200 can be formed with the digits 0,...
Answer is 6..
the possibilities are 213,231,312,321,1023 and 1032
the possibilities are 213,231,312,321,1023 and 1032
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Community Answer
How many numbers between 200 and 1200 can be formed with the digits 0,...
B) 14 combinations are possible.
Possible combinations- 201, 203, 210, 213, 230, 231, 301, 302, 310, 312, 320, 321, 1023 and 1032.
Possible combinations- 201, 203, 210, 213, 230, 231, 301, 302, 310, 312, 320, 321, 1023 and 1032.
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How many numbers between 200 and 1200 can be formed with the digits 0, 1, 2, 3 (repetition of digits not allowed?a)6b)18c)2d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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