CA Foundation · Quantitative Aptitude · Permutations and Combinations
How many different 5-digit numbers can be formed using all the digits 1, 1, 2, 2, 3 exactly once each as given?
The answer is 30. Using all five digits 1, 1, 2, 2, 3, the count is 5! divided by 2! for the repeated 1s and 2! for the repeated 2s, giving 120/4 = 30 distinct numbers.
- A30Correct
- B60
- C120
- D15
Explanation
All 5 digits are used, with 1 repeated twice and 2 repeated twice. Number of arrangements = 5!/(2! 2!) = 120/4 = 30. No digit is zero, so every arrangement is a valid 5-digit number. The option 60 divides by only one 2!.
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