And that's because of all of the different patterns we can permute.

这是因为我们可以改变所有不同的模式。

That however, would grossly overcount the  total number since all the different ways you can permute these four items would be  counted separately.

然而，这高估总数，因为排列这四个项目的所有不同方式都将单独计。

It turns out though, if you think about the group which permutes the roots of such a polynomial, there's something about the nature of this group that reveals that no quintic formula can exist.

但事实证明， 如果你考虑对这样一个多项式的置换的群，就发现该群的性质表明不存在五次公式。

This particular isomorphism between cube rotations and permutations of four objects is a bit subtle, but for the curious among you, you may enjoy taking a moment to think hard about how the rotations of a cube permute its four diagonals.

立方体旋转和四个对象的排列之间的这种特殊同构有点微妙，但对于好奇的人来说， 您可能喜欢花点时间认真思考立方体的旋转如何排列其四个对角线。