Recent content by ZZ Specs

Yes, 5C40 gives 658,008 ways of picking 5 marbles out of 40. Does that not ignore certain conditions of non-repetition though? Once you draw the first marble, the probabilities of the next draw have already changed. I believe it is correct that there are 5! = 120 ways of picking 3 red and 2...

Hello all! Sorry for the late response, hope you're all still around. Let's pretend I want exactly 3 out of 5, since it's not too hard (I think) to then add the probabilities of 3/5 +(or) 4/5 +(or) 5/5. I can work it out on a tree, for instance: 19/40*(..conditional probabilities..) +...

Let's pretend I have a bag of 40 marbles. 19 marbles are red, 21 marbles are blue. If I randomly pick 5 marbles out of the bag, what is the probability that 3 of those 5 marbles are red?

I believe so, that the order of a subgroup must divide the order of its group. I know that <σ> is a group (all cyclic elements form groups, correct?), but do we have any other groups to compare in this situation? I'm not used to working with permutations, especially in view of groups.

Thank you very much for all your help though!

In that case, why can we say that a cyclic group of order 7 is impossible? I was thinking that because σ lies in S5 (i.e. |σ| ≤ 6 ), σ^k must equal the identity for some k < 7. Is there another way to establish this?

Is it valid to say that because σ is in S5, the order of sigma is at most 6?

Thank you for your reply, much appreciated. Could you further explain what property shows that "either σ = id or S5 contains a cyclic group of order 7"?

Is there a theorem or any useful application for knowing the order of a permutation belonging to the symmetric group Sn? For example, Lets say σ is a permutation belonging to S5; i.e. σ is a permutation of {1,2,3,4,5}. If we are given that σ^7 = I (the identity permutation), then how can we...

Oh of course. Wow, I didn't see that. So the solution set could be considered: Assuming a_i in G for all i in the index set I, {g in G : g lies in the intersection ∏i in I {g = a_i h a_i-1 for some h in H} } Not sure if ∏ is the best symbol to represent intersection, but for now let's go...

Hi all, Suppose H is a subgroup of G. For g in G, define fg : G/H > G/H by fg (aH) = gaH for a in G, where G/H is the set of left cosets of H in G. What is the difference between these two statements: 1) for a given aH in G/H, the set {g in G : fg(aH) = aH } 2) set {g in G : fg = the...

Homework Statement Suppose H is a subgroup of G. For g in G, define fg : G/H > G/H by fg (aH) = gaH for a in G, where G/H is the set of left cosets of H in G. I know that fg is a well-defined permutation. However, we have not established (yet) that G/H is a group. 2 parts to the...

I see, and I am referring strictly to the appearance of the astronaut. Interesting phenomenon. When you say "they 'see' the light traveling towards them at an infinite speed", is this because as soon as they see the light being emitted, it immediately reaches their eyes (the light beam traveling...

You are entirely correct, my apologies. I read the article when you first posted it but missed the session on length contraction this time around. This is what I've now gathered from it and from your explanation, at its most basic level: The speed of light is constant. But different frames...

Mr. Simon Bridge, thank you for the link. It contained many helpful resources. Mr. ghwellsjr, thank you for your detailed reply. That was extremely informative and cleared up a whole lot of info on the subject, I very much appreciate you taking the time to explain this all to me. It is very...