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=(n!)/(\left(n-k\right)!)`

Where:

`n!=\text{ n factorial}`

the value of "n!" is given by:

`n!=1*2*3*...* n`

From the given problem we have:

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

Substituting the values we get:

`nPk=(15!)/(\left(15-4\right)!)`

Solving the operations:

`nPk=(15!)/(11!)=(1*2*3*4*..*15)/(1*2*3*4*..*11)`

Solving the products:

`nPk=32760`

Therefore, there are 32760 permutations.