Engineering Board Exam Reviewer · Combinations · hard

Three vertices are chosen from a regular octagon to form a triangle. How many of these triangles have no side in common with the octagon?

  1. 56
  2. 16
  3. 32
  4. 8

Answer

B. 16

Solution

Total triangles: 8C3=56. Triangles with two octagon sides (three consecutive vertices): 8. Triangles with exactly one octagon side: 8×4=32 (choose the side, then a vertex not adjacent to it). So 56-8-32=16.

More Combinations questions

  1. How many non-negative integer solutions does x+y+z=10 have?
  2. If nC2=66, find n.
  3. A team of 3 players is selected from 10 players, and then one of the three is named captain. In how many ways can this be done?
  4. A bag has 6 red and 5 blue balls. In how many ways can 4 balls be drawn so that both colors are present?
  5. The letters of the word EQUATION are used to form 5-letter arrangements (no repetition) that contain exactly 3 vowels and 2 consonants…
  6. How many 5-card poker hands from a standard 52-card deck contain exactly 2 aces?
  7. A committee of 4 is chosen from 7 men and 5 women. In how many ways can it be chosen if it must include at least 2 women?
  8. In how many ways can 6 items be chosen from 8 different items?
  9. A committee of 3 is to be chosen from 12 members. In how many ways can this be done?
  10. In how many ways can a committee of 4 be selected from a group of 10 people?

All Combinations questions