Started 3 weeks ago by sakshi jaiswal in
FOR THIS ONE MY SOLUTION IS = 3C1 * 8C2 = 84 IS COMMING BUT THE ANS IS 64 SO AM I DOING ANY THING WRONG
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3 Replies
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Replied 8 months ago
Let's look at this problem again. You need to select 3 players such that at least 1 is from Croatia. It can be tricky tackling it directly, so we'll use complementary counting instead. Total ways to select any 3 players from 9 players: [ \binom{9}{3} = 84 ] Ways to select 3 players with no one from Croatia: There are 2 from France and 4 from the Netherlands (6 players in total). [ \binom{6}{3} = 20 ] Use complementary counting: Subtract the above result from the total: [ 84 - 20 = 64 ] Therefore, there are 64 ways to select 3 players such that at least 1 is from Croatia. Your initial calculation missed considering the complementary counting approach.