Question

Find the number of different ways that an instructor can choose 4 students from a class of 23 students for a field trip.

Answer 1

We have to find how many ways we can group 23 students in groups of 4.

This can be calculated as a combination of 23 in 4, as order does not matter and there is no repetition.

We can calculate it as:

`\begin{gathered} C(n,r)=(n!)/(r!(n-r)!) \\ C(23,4)=(23!)/(4!(23-4)!) \\ C(23,4)=(23!)/(4!19!) \\ C(23,4)=(23\cdot22\cdot21\cdot20)/(4\cdot3\cdot2\cdot1) \\ C(23,4)=(212520)/(24) \\ C(23,4)=8855 \end{gathered}`

Answer: there are 8855 ways.