Question

Two teams are to play a series of five matches between them. A match ends in a win, loss or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is
(a) 81
(b) 243
(c) 486
(d) none of these

Answer 1

Hint: We need to find n which is the smallest group of people in which only one person predicts the result correctly for all matches. So here the smallest group of people will be the total number of possible outcomes for 5 matches.

Complete step-by-step answer:
It is mentioned in the question that 5 matches are to be played and each match can have either of the three results. Also it is given that every member of a group predicts a different result for different matches. So since every forecast is different we need to have a smallest possible group for one of them to get it correctly.
So here the smallest group will be the total number of possible outcomes. And we will find the total possible outcomes from the fundamental principle of counting.
Now the total number of possible outcome for 5 matches$=3\times 3\times 3\times 3\times 3=243$
Hence the smallest group will have 243 people. Hence n is 243.
So the correct answer is option (b).

Note: The fundamental principle of counting is a way to figure out the number of outcomes in a probability problem. Basically, we multiply the events together to get the total number of outcomes.