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Problem of the Day #282: The Albert T. Gural Fanclub December 26, 2011

Posted by Seungln in : potd , trackback

The Albert T. Gural Fanclub currently has $7$ members: Saketh, Sreenath, Albert, Billy, SeungIn, Arjun, Aziz. Because this club only has $7$ members so far, each member (except Albert) decides to recruit more people. Saketh, Sreenath, Billy, SeungIn, Arjun and Aziz have the same recruiting abilities, and are going to be able to recruit $1$, $2$, $3$, $4$, $5$ or $6$ new members, not necessarily in that order, with equal probability. The six members decide to split the pile of $\$ 21,000$ proportional to the amount of members each person recruited. If SeungIn suddenly receives temporary foresight that lasts long enough to show him that Arjun will only recruit $2$ people, how much money can he expect to receive?

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