Chapter 13.10, Problem 37SR

To determine

The statement is permutation or combination then solve.

How many ways can $4$ shirts be chosen from $10$ shirts to take on a trip?

Answer to Problem 37SR

These is the combination situation and there are total $210$ ways of choosing $4$ shirts from $10$ shirts for a trip.

Explanation of Solution

This is the combination situation.

For choosing the $4$ shirts from $10$ shirts for a trip, the order is not important so the number of ways choosing the shirts for a trip is as follows,

  $\begin{array}{l}C\left(10,4\right)=\left(\frac{\mathrm{10.9.8.7}}{\mathrm{1.2.3.4}}\right)\\ C\left(10,4\right)=\left(\frac{5040}{24}\right)\\ C\left(10,4\right)=210\end{array}$ .

So there are total $210$ ways of choosing $4$ shirts from $10$ shirts for a trip.

Conclusion:

Hence, these is the combination situation and there are total $210$ ways of choosing $4$ shirts from $10$ shirts for a trip.