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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations

Which of the following equals 6! − 5! ?

6! − 5! equals 5 × 5!. Writing 6! as 6 × 5! and factoring out 5! gives 5!(6 − 1) = 5 × 120 = 600, which matches 720 − 120. Factorial subtraction does not simplify to 1!.

  1. A5 × 5!Correct
  2. B1!
  3. C5!
  4. D6 × 5!

Explanation

6! = 6 × 5!, so 6! − 5! = 5!(6 − 1) = 5 × 5! = 600. Option 5! = 120 wrongly treats the difference as 5!. Check: 720 − 120 = 600.

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