CA Foundation · Quantitative Aptitude · Permutations and Combinations
Simplify: (n + 2)! ÷ n! when n = 6.
The value is 56. Writing (n+2)! as (n+2)(n+1)n! and cancelling n! leaves (n+2)(n+1). With n = 6 this is 8 × 7 = 56. The option 42 wrongly uses (n+1)n, which would be 7 × 6.
- A8
- B42
- C56Correct
- D72
Explanation
(n+2)!/n! = (n+2)(n+1). For n = 6 this is 8 × 7 = 56. Checking: 8! = 40320 and 6! = 720, and 40320/720 = 56. The option 42 is 7 × 6, which is (n+1)n and uses the wrong terms.
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