GCEFurther MathematicsPermutations and Combinations2024
How many 4-digit numbers greater than 4000 can be formed using the digits 2, 3, 4, 5, 6 if repetition is not allowed?
A72
B96CORRECT
C120
D144
AI
Toaster Teacher
Why the answer is B, and why the others tempt you.
For a 4-digit number greater than 4000, the first digit must be 4, 5, or 6 (3 choices). The remaining 3 digits are chosen from the 4 remaining digits: 4 × 3 × 2 = 24 ways. Total = 3 × 24 = 72. Wait — re-checking: first digit has 3 choices (4,5,6), then 4 remaining digits for 2nd place, 3 for 3rd, 2 for 4th: 3 × 4 × 3 × 2 = 72. The answer is A: 72.
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