How many numbers between 200 and 1200 can be formed with the digits 0,1,2,3 if repetition of digits is allowed?
A. 48
B. 63
C. 32
D. 14
E. 20
My Solution:
First, i'm splitting 3-digit and 4-digit sets like 201-999 as set-1 and 1000-1199 as set-2
For set-1, Hundred-digit * tens-digit * units-digit = 2 possibilities * 4 possibilities * 4 possibilities => 32
Similarly for set-2, Thousand-digit * Hundred-digit * tens-digit * units-digit = 1 possibility * 2 possibilities * 4 possibilities * 4 possibilities => 32
Therefore, 32+32 in total = 64.
But the OA is 63. Why do we subtract the total by 1 here? Can someone clarify my doubt and explain? This is not a GMAT problem for sure. I'm very weak in this subject and i'm working hard on it to build my fundamentals. I hope my steps to solve the problem are correct.
A. 48
B. 63
C. 32
D. 14
E. 20
My Solution:
First, i'm splitting 3-digit and 4-digit sets like 201-999 as set-1 and 1000-1199 as set-2
For set-1, Hundred-digit * tens-digit * units-digit = 2 possibilities * 4 possibilities * 4 possibilities => 32
Similarly for set-2, Thousand-digit * Hundred-digit * tens-digit * units-digit = 1 possibility * 2 possibilities * 4 possibilities * 4 possibilities => 32
Therefore, 32+32 in total = 64.
But the OA is 63. Why do we subtract the total by 1 here? Can someone clarify my doubt and explain? This is not a GMAT problem for sure. I'm very weak in this subject and i'm working hard on it to build my fundamentals. I hope my steps to solve the problem are correct.
