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

Sagot :

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:

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

Answer: there are 8855 ways.

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