Chapter 11.6, Problem 29E

To determine

To calculate: thechoices for seating the 6 groups in the restaurant.

Answer to Problem 29E

the choices for seating the 6 groups in the restaurant is $665280$ .

Explanation of Solution

Given :

Total identical tables = $12$

Accepts reservation tables = $6$

Formula used:

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

Calculation : to find the choices for seating we have to take 6 tables among 12 tables.

Then put $n=12$ and $r=6$ .

  $\begin{array}{l}P{}_6=\frac{12!}{\left(12-6\right)!}\text{ [substitue n by 12 and r by 6]}\\ P{}_6=\frac{12·11·10·9·8·7·6!}{6!}\text{ [subtract, expand factorial and divide out common factors}]\\ P{}_6=12·11·10·9·8·7\\ P{}_6=665280\text{ [multiply]}\end{array}$

Hence,the choices for seating the 6 groups in the restaurant is $665280$ .