Question

a math club has 4 students, and 3 will be chosen to compete in a specific order at a regional competition. how many different ways can the 3 students be chosen and arranged?
\\( _4p_3 = ? \\)

Explanation:

Step1: Recall permutation formula

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$ where $n=4$, $k=3$.

Step2: Calculate factorials

$4! = 4×3×2×1=24$, $(4-3)! =1! =1$.

Step3: Compute result

$P(4,3)=\frac{24}{1}=24$.

Answer:

24