Question

Find the number of different ways that an instructor can choose 4 students from a class of 13 students for a field trip. Hint: The order of selection of the students for the trip does not matter.

Answer 1

There are 715 different ways to choose 4 students from a class of 13 for a field trip, calculated using the combination formula nCr = n! / (r! * (n-r)!).

Step-by-step explanation:

The student has asked how to calculate the number of ways to choose 4 students from a class of 13 for a field trip, where the order of selection does not matter. This is a combinatorics problem, and the solution involves calculating a combination, not a permutation because the order of selection is irrelevant.

To find the number of combinations of 4 students out of 13, we use the formula nCr, which represents the number of combinations of r items taken from a set of n items and is calculated using the formula nCr = n! / (r! * (n-r)!), where! denotes factorial.

For this problem, n is 13 and r is 4, so we have:

• 13! / (4! * (13-4)!) = 13! / (4! * 9!)
• This simplifies to (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)
• After simplification, we obtain 715

Therefore, there are 715 different ways to choose 4 students from a class of 13 for a field trip.