How many numbers greater than 1000, but not greater than 4000 can be formed with the digits 2,1,2,3,4 repetition of the digit being allowed?a)374b)375c)376d)noneCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Numbers greater than 1000 but less than 4000 formed with digit 0,1,2,3,4 will be
3.5.5.5+1-1 = 375-1+1
= 375

Answer

To find the number of numbers greater than 1000 but not greater than 4000 that can be formed with the digits 2, 1, 2, 3, 4 (repetition of the digit being allowed), we can break down the problem into different cases and use the concept of permutations.

Case 1: The thousands place is 1.
In this case, the remaining three digits can be arranged in 3! = 6 ways, giving us 6 numbers.

Case 2: The thousands place is 2.
In this case, the remaining three digits can be arranged in 3! = 6 ways, giving us 6 numbers.

Case 3: The thousands place is 3.
In this case, the remaining three digits can be arranged in 3! = 6 ways, giving us 6 numbers.

Case 4: The thousands place is 4.
In this case, the remaining three digits can be arranged in 3! = 6 ways, giving us 6 numbers.

Therefore, the total number of numbers that can be formed is:
6 (Case 1) + 6 (Case 2) + 6 (Case 3) + 6 (Case 4) = 24.

However, we need to consider that if the number is exactly 4000, it should not be counted as it is not greater than 4000. Therefore, we subtract 1 from the total.

Total number of valid numbers = 24 - 1 = 23.

Therefore, the correct answer is option 'D' (none).

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