GCEFurther MathematicsPermutations and Combinations2021

How many 4-digit numbers greater than 4000 can be formed using the digits 2, 3, 4, 5, 6 if repetition is not allowed?

A54
B72CORRECT
C96
D120
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Why the answer is B, and why the others tempt you.
The first digit must be 4, 5, or 6 to ensure the number exceeds 4000 (3 choices). The remaining 3 positions are filled from the 4 leftover digits without repetition: 4 × 3 × 2 = 24 ways. Total = 3 × 24 = 72.
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