CA Foundation · Quantitative Aptitude · Permutations and Combinations
How many 4-digit numbers greater than 5000 can be formed using the digits 0, 2, 5, 6, 7, 8 if no digit is repeated?
The answer is 240. The first digit must be at least 5, so 5, 6, 7 or 8 gives 4 choices. The remaining three places are filled from the 5 left-over digits without repetition in 5 × 4 × 3 = 60 ways, so 4 × 60 = 240.
- A180
- B240Correct
- C120
- D300
Explanation
The thousands digit must be 5, 6, 7 or 8, giving 4 choices. The remaining 3 places are filled from the other 5 digits (including 0) in 5 × 4 × 3 = 60 ways. Total = 4 × 60 = 240. Option 300 wrongly uses 5 choices for the first digit by including 2, which would give a number below 5000.
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