Project ForgeGiven digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
- A50
- 51
- C52
- D54
Explanation
Available copies: digit 2 x2, digit 3 x3, digit 4 x4. For the number to exceed 3000 the first digit must be 3 or 4 (2 choices), with the other 3 positions free from {2,3,4}: 2x3^3 = 54 unrestricted sequences. Subtract sequences that use more copies of a digit than are available: using 2 three times (only possible with the free digit = the leading digit, giving 3222 and 4222, 2 sequences) and using 3 four times (only 3333, 1 sequence, still counted since its leading digit is 3). No sequence violates both simultaneously. Valid count = 54 - 2 - 1 = 51.
Source: GATE ME 2010 (2010)
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