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  4. Two teams are to play a series of 5 matches between them. A match ends in a win or loss or draw. 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

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Q. Two teams are to play a series of $5$ matches between them. A match ends in a win or loss or draw. 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

Permutations and Combinations

Solution:

The smallest number of people.
$=$ total number of possible forecasts
$=$ total number of possible results
$=3 \times 3 \times 3 \times 3 \times 3$