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CA Foundation · Quantitative Aptitude · Permutations and Combinations

How many distinct 6-digit numbers can be formed using all the digits 1, 1, 2, 2, 3, 3 (each digit used exactly the number of times given)?

The answer is 90. Six digits are arranged, with each of 1, 2 and 3 appearing twice. The count is 6! divided by 2!·2!·2!, which is 720 divided by 8, giving 90 distinct numbers.

  1. A180
  2. B90Correct
  3. C720
  4. D60

Explanation

Six digits with 1, 2 and 3 each repeated twice give 6!/(2!·2!·2!) = 720/8 = 90. The value 720 is wrong because it treats all digits as distinct. The value 180 divides only by two factorials of 2!.

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