RJC 2001 Term III Common Test Q1
Four-digit numbers are to be formed from the digits {1, 2, 3, 4, 5, 6}. Find the number of ways this can be done if
i) no digit may appear more than once; [1]
ii) any digit may be repeated; [1]
iii) there is at least one repeated digit, but no digit may appear more than twice. [4]
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Answer:
i) 6P4 = 360
ii) 6*6*6*6 = 1296
iii) Case only 1 digit repeated: (6C1 * 5C2) * (4! / 2!) = 720
Case 2 repeated digits: 6C2 * (4!/2!2!) = 90
Summing up:
720 + 90 = 810
