Question

Out of 10 students, 2 will be chosen to ride in a car instead of a van on an upcoming field trip. Which statement best describes this situation?
A. There are 10P2 = 90 ways the students can be chosen to ride in the car because the order in which the students are chosen matters.

B. There are 10C2 = 45 ways the students can be chosen to ride in the car because the order in which the students are chosen matters.

C. There are 10P2 = 90 ways the students can be chosen to ride in the car because the order in which the students are chosen doesn’t matter.

D. There are 10C2 = 45 ways the students can be chosen to ride in the car because the order in which the students are chosen doesn’t matter.

Answer 1

Answer:

D

Step-by-step explanation:

Firstly, since it is a selection question, we shall be using a combination approach.

So here we are trying to select the best answer that describes that 2 out of 10 students are selected.

Let’s consider the scenario below;

selecting r out of n can be resolved using the combination nCr

= n!/(n-r)!r!

Now in this case, our n = 10 and r = 2.

Thus, 10C2, we have ;

10!/(10-2)!2! = 10!/8!2! = (10 * 9 * 8!)/8!2! = (10 *9)/2! = 90/2 = 45

Thus, 10C2 = 45

Here, the order of selection does not matter as we can select in random fashion. This makes option D correct