The ballot problem. in an election, candidate a receives n votes and candidate b receives m votes, where n> m. assuming that all of the (n+m)! /n! m! orderings of the votes are equally likely, let
pn, m
denote the probability that a is always ahead in the counting of the votes.(a) compute
p2,1,p3,1,p3,2,p4,1,p4,2,p4,3
. (b) find
pn,1,pn,2
. (b) find pn,1,pn,2.
(c) on the basis of your results in parts (a) and (b), conjecture the value of
pn, m
. (d) derive a recursion for
pn, m
in terms of
pn−1,m
and
pn, m−1
by conditioning on who receives the last vote.(e) use part (d) to verify your conjecture in part (c) by an induction proof on n+m.

linear pair postulates

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yes, i heard the "tea" with james charles and a few other beauty gurus. i believe charles is in the wrong and i believe tati the most. tati didn't lie about james charles but may have exaggerated because he never sexually assaulted anyone. jeffery star is a really good friend to all and out anyone that needs it, until you mess with one of his "sisters"! james will never rise over jeffery or tati, he's way to sensitive and dramatic to rise about them. i think all three of them will make up and be friends again because they always get over it.

i hope this with your

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