Chapter 12, Problem 24SGR

a.

To determine

To state: that to arrange the students is permutation or combination.

Answer to Problem 24SGR

To arrange the students is permutation.

Explanation of Solution

Given information:

Total students: $7$

to arrange the students, the students order is important.

Thus, to arrange the students is permutation.

b.

To determine

To find: the ways to arrange the students.

Answer to Problem 24SGR

the ways to arrange the students is $5040$ .

Explanation of Solution

Given information:

Total students: $7$

Formula used:

  $n!=n\left(n-1\right)\left(n-2\right)\mathrm{...3}·2·1$

Calculation: to find the ways to arranged the students, substitute the value of n and multiply,

  $\begin{array}{l}n!=n\left(n-1\right)\left(n-2\right)\mathrm{...3}·2·1\\ 7!=7·6·5·4·3·2·1\text{ [}n=7]\\ 7!=5040\text{ [multiply]}\end{array}$