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The result of 8 matches (win,loss or draw) are to be predicted. The number of different forecast containing exactly 6 correct results are?
Most Upvoted Answer
The result of 8 matches (win,loss or draw) are to be predicted. The nu...
Number of different forecasts containing exactly 6 correct results


There are 3 possible outcomes for each match - win, loss or draw. Therefore, there are 3^8 = 6561 possible forecasts for the 8 matches.


Calculating the number of forecasts with exactly 6 correct results


In order to calculate the number of forecasts with exactly 6 correct results, we need to consider the number of ways we can choose 6 out of the 8 matches to predict correctly. This can be calculated using the combination formula:


nCr = n! / (r! * (n-r)!)


where n is the total number of matches (8), and r is the number of matches we want to predict correctly (6).


Using this formula, we get:


8C6 = 8! / (6! * (8-6)!) = 28


Calculating the number of forecasts with 2 incorrect results


Now that we know there are 28 possible forecasts with exactly 6 correct results, we need to calculate the number of forecasts with 2 incorrect results. In order to do this, we need to consider the number of ways we can choose 2 out of the 8 matches to predict incorrectly. This can be calculated using the combination formula:


nCr = n! / (r! * (n-r)!)


where n is the total number of matches (8), and r is the number of matches we want to predict incorrectly (2).


Using this formula, we get:


8C2 = 8! / (2! * (8-2)!) = 28


Calculating the total number of forecasts with exactly 6 correct results


Now that we know there are 28 possible forecasts with exactly 6 correct results and 28 possible forecasts with 2 incorrect results, we can calculate the total number of forecasts with exactly 6 correct results:


Total number of forecasts with exactly 6 correct results = 28 * 28 = 784


Conclusion


Therefore, there are 784 different forecasts containing exactly 6 correct results.
Community Answer
The result of 8 matches (win,loss or draw) are to be predicted. The nu...
Any 6 out of 8 will give correct result in one way I.e.., 8c6 other two will give wrong result each in 2 different ways. 8c6*1*2*2=112
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The result of 8 matches (win,loss or draw) are to be predicted. The number of different forecast containing exactly 6 correct results are?
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