Question

In one day, a salesman plans to visit 6 out of 11 companies that are in the neighborhood.How many ways can he pick the visits?(He visits one at a time and makes a list to start)

Answer 1

From the question, we can deduce the following:

Number of companies in the neighbourhood = 11

Number of companies he plans to visit = 6

Let's determine the number of ways he can the the company he visits.

To determine the number of ways, apply the permutation formula:

$_nP_r=\frac{n!}{n-r!}$

Where:

n = 11

r = 6

Thus, we have:

$\begin{gathered} _{11}P_6=\frac{11!}{(11-6)!} \\ \\ _{11}P_6=\frac{11!}{5!} \\ \\ _{11}P_6=\frac{11\times10\times9\times8\times7\times6\times5!}{5!} \\ \\ _{11}P_6=11\times10\times9\times8\times7\times6 \\ \\ _{11}P_6=332640 \end{gathered}$

Therefore there are 332640 ways he can pick the visits.

ANSWER:

332640 ways