Exercise · ZW-FACTORIAL-007 · ★★☆ Intermediate
Simplify \(\dfrac{n!}{(n-2)!}\) for \(n\ge 2\).
Choose one option.
Show answer
- D. \(n(n-1)\)
Explanation
\(n!=n(n-1)(n-2)!\), so the quotient is \(n(n-1)\). For \(n=7\): \(7\cdot 6=42=7!/5!\).
Review the concept: Factorial
The factorial of an integer \(n\ge 0\), written \(n!\), is the product of the positive integers less than or equal to \(n\); that of zero is one by convention.
\[n!=n(n-1)\cdots 2\cdot 1,\quad 0!=1\]
More practice problems: factorial
- ZW-FACTORIAL-001 Compute 5!.
- ZW-FACTORIAL-002 In how many ways can 6 different people line up in a row?
- ZW-FACTORIAL-003 Compute (6!)/(4!).
- ZW-FACTORIAL-004 Why is 0! defined as 1?
- ZW-FACTORIAL-005 For n≥ 0, which equals (n+1)!?
- ZW-FACTORIAL-006 Compute (8!)/(6! 2!).
- ZW-FACTORIAL-008 Words of 4 letters are formed from A, B, C, D (no repetition). How many start with A?
- ZW-FACTORIAL-009 Five people (3 men and 2 women) line up with the two women next to each other. In how many ways?