CA Foundation · Quantitative Aptitude · Permutations and Combinations
How many 4-digit numbers greater than 5000 can be formed using the digits 0, 3, 5, 6, 8, 9 if digits may be repeated?
The answer is 864. The thousands digit must be 5, 6, 8 or 9, giving 4 choices. The remaining three places each have 6 choices because repetition is allowed. So the count is 4 × 6 × 6 × 6 = 864.
- A648
- B864Correct
- C1080
- D720
Explanation
For the number to exceed 5000, the thousands digit must be 5, 6, 8 or 9, giving 4 choices. Each of the other three places can take any of the 6 digits since repetition is allowed: 6 × 6 × 6 = 216. Total = 4 × 216 = 864. The value 720 comes from wrongly using 5 digits for the later places.
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