Chapter 11.6, Problem 26E

To determine

To calculate: the different possible lineup there for Monday night.

Answer to Problem 26E

the different possible lineup there for Monday night is $32760$ .

Explanation of Solution

Given :

Total comedy show = $15$

Choose shows = $4$

Formula used:

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

Calculation : tofind thedifferent possible lineups for we have to choose 4 lineups among 15, so put the value in the above formula.

  $\begin{array}{l}P{}_4=\frac{15!}{\left(15-4\right)!}\text{ [substitue n by 15 and r by 4]}\\ P{}_4=\frac{15!}{11!}\text{ [subtract, expand factorial and divide out common factors}]\\ P{}_4=15·14·13·12\\ P{}_4=32760\text{ [multiply]}\end{array}$

Hence,the different possible lineup there for Monday night is $32760$ .