CA Foundation · Quantitative Aptitude · Permutations and Combinations
A mobile PIN has 4 digits chosen from 0 to 9 with repetition allowed. How many PINs have at least one repeated digit?
The answer is 4960. All 4-digit PINs number 10^4 = 10000, and those with all distinct digits number 10 × 9 × 8 × 7 = 5040. Subtracting the distinct ones from the total gives PINs with at least one repeat: 4960.
- A5040
- B4960Correct
- C10000
- D5000
Explanation
Total PINs = 10^4 = 10000. PINs with all digits different = 10 × 9 × 8 × 7 = 5040. PINs with at least one repeated digit = 10000 − 5040 = 4960. Option 5040 is the count with no repeated digit.
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