Yes they can be, the two definitions are not related.
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The number is 5! = 120
when the signals are symmetric then this signals are gaussian In statistics, the Gaussian curve, also known as the Normal curve, is symmetrical.
Symmetric
yes, it is both symmetric as well as skew symmetric
Humans are symmetric (look in a mirror and imagine a vertical line going from the center of your forehead to the floor between your feet). Also, the letters W, T, Y, U, O, A, H, X, V, and M are symmetric.