Question

there are 5 customers currently present in a coffee shop. three of the customers are waiting in line at the front register. how many different lines of customers are possible?
○ 6
○ 10
○ 60
○ 120

Explanation:

Step1: Identify permutation scenario

We need to find ordered arrangements of 3 customers chosen from 5, which is a permutation problem. The formula for permutations is $P(n,k)=\frac{n!}{(n-k)!}$, where $n=5$ (total customers) and $k=3$ (customers in line).

Step2: Calculate factorial values

First, compute $n!=5!=5\times4\times3\times2\times1=120$, and $(n-k)!=(5-3)!=2!=2\times1=2$.

Step3: Compute permutation result

Substitute values into the permutation formula:
$P(5,3)=\frac{5!}{(5-3)!}=\frac{120}{2}=60$

Answer:

60 (Option: 60)