Bunuel wrote:
Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)
(A) 210
(B) 560
(C) 840
(D) 1260
(E)}1680
An octahedron has 8 triangles.
So, we have to fix 2 faces, before applying colours.
So, the first face that can be fixed can be any of the 8 faces but each face will be similar , so 8/8 ways.
Now, when you have fixed one face, the three adjoining faces are similar, so we have 7 colours for the second face, so 7/3.
Now, you can place any color anywhere, it will be a different arrangement, so 6!
Total = (8/8)*(7/3)*6!=1*7*6*5*4*2=1680
E