Question

evaluate the given expression.
p(k, 2)

Explanation:

Step1: Recall permutation formula

The permutation formula is $P(n, r) = \frac{n!}{(n-r)!}$

Step2: Substitute $n=k, r=2$

$P(k, 2) = \frac{k!}{(k-2)!}$

Step3: Simplify factorial expression

$\frac{k!}{(k-2)!} = k\times(k-1)\times\frac{(k-2)!}{(k-2)!} = k(k-1)$

Step4: Expand the product

$k(k-1) = k^2 - k$

Answer:

$k^2 - k$ (or $k(k-1)$)