We 5000 People .

it is clear that all the people can Win $50, because the Count of The $50 Certificates is The Maximum count and it is bigger from count of people.

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So We Will remove the $50 Certificates and going on by this conditions :

1 - $100,000 certificate

5 - $1,000 certificates

10-$500 certificates

1,000 - $100 certificates

Now The N(S) = 1 *100,000$ + 5 * 1000$ + 10 * 500$ + 1000 * 100$

So The N(S) = 210,000 $

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P(Each Person Win 100,000$) =

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and so on ...