In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the
top 3 will be awarded medals, then how many groups of medal winners are possible?
(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

• I get 8C3 = 56
  
  I think that if you do 8C6 * 6C3 you are counting many groups more than once:
  
  Let’s say you have A, B ,C , D, E, F, G, H, and A and B do not qualify for the final: we have 6C3 = 20 possibilities (eg, CDE, CDF).
  Now we leave out G and H, you get another 20 possibilities.
  You can do this 8C6 = 28 times, but many groups get repeated. In our example CDE will be a group that appears when A and B don’t qualify and also appear when G and H don’t qualify or when A and G don’t qualify. That’s why we are counting all groups many times.
  
  It does not matter that only 6 got to the final, we have 8 elements to play with and we have to put them into groups of 3. Going from the semifinal to the final is not adding any restriction (eg A never qualifies). And if there was a restriction the answer could have never be more than 8C3= 56
• 11 years agoHelpfull: Yes(14) No(2)
• 6 candidates can selected from 8 in 8C6=28 ways.
  then for every such selection 3 can be selected from 6 in 6C3 ways=20 ways
  so, total no. of groups of medal winners is 28*20=560
  thank you..
• 14 years agoHelpfull: Yes(8) No(13)
• B. 56
• 14 years agoHelpfull: Yes(2) No(5)
• (8C6)*(6C3) = 560
• 14 years agoHelpfull: Yes(2) No(6)
• 56
• 14 years agoHelpfull: Yes(1) No(5)
• (B) 56
• 14 years agoHelpfull: Yes(0) No(5)
• A)20 Selecting and arranging 3 out of 6 finalists is 6P3 = 20
• 14 years agoHelpfull: Yes(0) No(7)
• what is the crt ans..??
• 9 years agoHelpfull: Yes(0) No(0)
• ans= 56 , 8c3
• 7 years agoHelpfull: Yes(0) No(0)