00:01
Now in this question, we look at a tetrahedrine, right? it's something like this, right? tetrahydrogen is, of course, something like this, right? it has six edges, right? it has six edges.
00:11
Now you ask a few questions, right? basically about how many ways are there to color the edges of this rectangular tetraudron, right? the first case is that, suppose you have n colors, right? if you have n colors are available to color this edges, how many ways you can color them.
00:28
And of course, each age is, has n possibilities, right? so you have six edges, that's of course, and part to the part to six, right? so that's not the number of ways.
00:38
And b question says, suppose you have only three colors and at the most two edges can be of any particular color.
00:46
So in other words, you know, the rest, you can have, you can have, at most two edges can be of any particular color.
00:55
That means you have, you know, you can have four, of them completely fixed, right? so in this case, you would have two, which i would like to choose.
01:04
And of course, each edge can have three choices, right? so that's nine.
01:09
And then if you have five edges fixed color, you have one edge which you can free choose, and that's you get three possibilities, right? and you have six, and then all fixed, you have only one possibility, right? so in the end, you put them together, you have basically 13, 13 ways, right? and then see, you look at three colors, still three colors available.
01:31
And at least the three edges have the same color...