Q1: a) As a fundraiser, a local GAA club runs a lotto-type draw in which 4 numbers are drawn from 20. As well as paying out a prize for a ticket with all four winning numbers, the club also refunds the price of any ticket which has none of the winning numbers. How many different tickets are there, and how many of them will have none of the four winning numbers?
Q1: a) As a fundraiser, a local GAA club runs a lotto-type draw in which 4 numbers are drawn from 20. As
well as paying out a prize for a ticket with all four winning numbers, the club also refunds the price
of any ticket which has none of the winning numbers. How many different tickets are there, and
how many of them will have none of the four winning numbers?
b) At the end of each season, two soccer leagues have an inter-league knock-out tournament between
the top 4 teams in each league – in which the winners of each league play the 4th team in the other
and the runners-up play the 3rd team from the other league. If one league has 10 teams and the
other league has 12 teams, how many different possible quarter-final line-ups are there?
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