Given digits 2,2,3,3,3,4,4,4,4 how many distinct 4 digit numbers greater than…
2010
Given digits 2,2,3,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed?
- A.
50
- B.
51
- C.
52
- D.
54
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Correct answer: B
First digit is either 3 or 4. We'll consider each case separately:
(1) First digit is 3: Then the rest of the numbers must come from the list: 2, 2, 3, 3, 4, 4, 4, 4 Therefore we may choose any 3-digit sequence except 222 and 333 for the rest of the digits. This shows there are 3*3*3 - 2 = 25 numbers in this case.
(2) First digit is 4: Then the rest of the numbers must come from the list 2, 2, 3, 3, 3, 4, 4, 4 Therefore we may choose any 3-digit sequence except 222 for the rest of the digits.
This shows there are 3*3*3 - 1 = 26 numbers in this case. Now, the total number is just 25 + 26 = 51.