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Two teams are to play a series of 5 matches between them. A match ends in a win or loss or draw for a term. 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
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two teams are to play a series of 5 matches between them. A match ends...
The smallest number of people
= total number of possible forecasts
= total number of possible results
= 3 * 3 * 3 * 3 * 3
= total number of possible forecasts
= total number of possible results
= 3 * 3 * 3 * 3 * 3
Most Upvoted Answer
Two teams are to play a series of 5 matches between them. A match ends...
Explanation:
Understanding the Problem:
- There are 5 matches in the series.
- Each match can end in a win, loss, or draw.
- No two people make the same forecast for all the matches.
- We need to find the smallest group of people where one person forecasts correctly for all matches.
Approach:
- Let's consider each match as a binary outcome (win/loss/draw).
- For each match, there are 3 possible outcomes.
- To guarantee that at least one person forecasts all matches correctly, we need to consider the worst-case scenario where each person makes a different forecast for each match.
Calculating the Number of Possible Forecasts:
- For each match, there are 3 possible outcomes.
- So, the total number of possible forecasts for 5 matches = 3 * 3 * 3 * 3 * 3 = 3^5 = 243.
Finding the Smallest Group:
- To find the smallest group where one person forecasts all matches correctly, we need to find the smallest power of 3 that is greater than or equal to the number of possible forecasts.
- The smallest power of 3 greater than or equal to 243 is 3^5 = 243.
Conclusion:
- The smallest group of people in which one person forecasts correctly for all the matches will contain 243 people.
Understanding the Problem:
- There are 5 matches in the series.
- Each match can end in a win, loss, or draw.
- No two people make the same forecast for all the matches.
- We need to find the smallest group of people where one person forecasts correctly for all matches.
Approach:
- Let's consider each match as a binary outcome (win/loss/draw).
- For each match, there are 3 possible outcomes.
- To guarantee that at least one person forecasts all matches correctly, we need to consider the worst-case scenario where each person makes a different forecast for each match.
Calculating the Number of Possible Forecasts:
- For each match, there are 3 possible outcomes.
- So, the total number of possible forecasts for 5 matches = 3 * 3 * 3 * 3 * 3 = 3^5 = 243.
Finding the Smallest Group:
- To find the smallest group where one person forecasts all matches correctly, we need to find the smallest power of 3 that is greater than or equal to the number of possible forecasts.
- The smallest power of 3 greater than or equal to 243 is 3^5 = 243.
Conclusion:
- The smallest group of people in which one person forecasts correctly for all the matches will contain 243 people.
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Community Answer
Two teams are to play a series of 5 matches between them. A match ends...
The smallest number of people
= total number of possible forecasts
= total number of possible results
= 3 * 3 * 3 * 3 * 3
= total number of possible forecasts
= total number of possible results
= 3 * 3 * 3 * 3 * 3
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Two teams are to play a series of 5 matches between them. A match ends in a win or loss or draw for a term. 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 isa)81b)243c)486d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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