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CA Foundation · Quantitative Aptitude · Permutations and Combinations

How many 5-digit numbers greater than 40000 can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition of any digit?

The answer is 360. For the number to exceed 40000 the first digit must be 4, 5 or 6, which gives 3 choices. The other four places are filled from the remaining five digits in 5P4 = 120 ways, so 3 × 120 = 360.

  1. A120
  2. B240
  3. C360Correct
  4. D720

Explanation

The first digit must be 4, 5 or 6, giving 3 choices. The remaining 4 places are filled from the other 5 digits in 5P4 = 120 ways. Total = 3 × 120 = 360. Option 720 comes from allowing 6 choices for the first digit, so it ignores the condition.

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