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William and Fred had both been nominated for president
of the local club. Under the rules of the club, an election for the presidency
had to be held and all 350 members were allowed to cast a single vote each.
After all the members who wished to vote had voted, the ballot box was
taken to the counting table. Each vote was taken out of the ballot box and
placed in two piles marked William and Fred. As each vote was placed on one
of the piles the tellers shouted out the current number of votes for each
candidate.
William won and in addition his vote had been ahead of
Fred's at every stage of the count. "There must be odds of a million to one
against that happening ," said Fred. "That's not true," said William," Now
that we know the number of votes we each received, we can calculate that
the chance of my leading throughout the count was exactly one in a hundred.
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How many members did not vote?
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