Grades 11-12 Video Solutions 2026-2026_11-12

Video Transcription

Video Summary

The number of triangular pyramids is <strong>72</strong>.  
Reason: to form a pyramid, the 4 chosen points cannot all lie on one face of the cube. So the 4 vertices must be distributed so that each of the relevant edges contributes points, with one edge contributing 2 points. Counting the possible selections gives:

- \(4 \times 3 \times 2 = 24\) ways to choose the first three points
- 6 choices for the fourth point
- divide by 2 because the two points on the same edge are interchangeable

So the total is:

\[
24 \times \frac{6}{2} = 72
\]

<strong>Answer: E, 72.</strong>

Keywords

triangular pyramids

cube vertices

combinatorics

counting selections

72