Question

flight attendants how many different ways can 4 flight attendants be selected from 10 flight attendants for a routine flight? there are ways to select the flight attendants.

Explanation:

Step1: Identify combination formula

The problem is a combination problem. The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here, $n = 10$ and $r=4$.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $10! = 10\times9\times8\times7\times6\times5\times4\times3\times2\times1$, $4! = 4\times3\times2\times1$, and $(10 - 4)!=6!=6\times5\times4\times3\times2\times1$. Then $C(10,4)=\frac{10!}{4!(10 - 4)!}=\frac{10\times9\times8\times7\times6!}{4\times3\times2\times1\times6!}$.

Step3: Simplify the expression

Cancel out the $6!$ terms. We have $\frac{10\times9\times8\times7}{4\times3\times2\times1}=\frac{5040}{24}=210$.

Answer:

210