Question

An outdoor summer camp offers its campers 14 activities. Campers make a schedule for their morning, afternoon, and evening sessions. They choose a different activity for each session.



How many different schedules are possible?

Answer options with 5 options
A.
42

B.
364

C.
728

D.
2184

E.
2744

Answer 1

To determine the number of different schedules possible for the campers at the outdoor summer camp, we need to consider the restrictions given: each camper selects from 14 activities and must choose a different activity for each of the three sessions (morning, afternoon, and evening).

Here's how the calculation is done:

1. For the **morning session**, a camper can choose any of the 14 activities.
2. For the **afternoon session**, since the camper must choose a different activity, they have 13 options remaining (14 total - 1 used in the morning).
3. For the **evening session**, the camper again must choose a different activity from the previous two sessions, leaving them with 12 options (14 total - 2 used in the morning and afternoon).

To find the total number of different schedules, we multiply the number of choices for each session together:

\[
\text{Total schedules} = 14 \text{ (morning)} \times 13 \text{ (afternoon)} \times 12 \text{ (evening)}
\]

Calculating this:

\[
14 \times 13 = 182
\]
\[
182 \times 12 = 2184
\]

Thus, the total number of different schedules possible is **2184**.

So the correct answer is:

**D. 2184**