Question

How many permutations can 4 students from a group of 15 be lined up for a photograph

Answer 1

Solving the We are asked to determine the number of permutation of 4 students taken from a set of 15.

The total number of permutations of "k" objects taken from a set of "n" elements is given by:

$nPk=\frac{n!}{\left(n-k\right)!}$

Where:

$n!=\text{ n factorial}$

the value of "n!" is given by:

$n!=1\times2\times3\times...\times n$

From the given problem we have:

$\begin{gathered} n=15 \\ k=4 \end{gathered}$

Substituting the values we get:

$nPk=\frac{15!}{\left(15-4\right)!}$

Solving the operations:

$nPk=\frac{15!}{11!}=\frac{1\times2\times3\times4\times..\times15}{1\times2\times3\times4\times..\times11}$

Solving the products:

$nPk=32760$

Therefore, there are 32760 permutations.