Question

question 11
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a pianist plans to play 6 pieces at a recital from her repertoire of 18 pieces.
how many different recital programs are possible?

Explanation:

Step1: Identify permutation need

Recital programs order matters, so use permutation.

Step2: Apply permutation formula

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$, where $n=18$, $k=6$.

Step3: Calculate the value

$P(18,6)=\frac{18!}{(18-6)!}=18×17×16×15×14×13$
$18×17=306$, $306×16=4896$, $4896×15=73440$, $73440×14=1028160$, $1028160×13=13366080$

Answer:

13366080