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The results of 8 matches (Win, Loss or Draw) are to be predicted. The number of different forecasts containing exactly 6 correct results is
- a)316
- b)214
- c)112
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The results of 8 matches (Win, Loss or Draw) are to be predicted. The ...
Solution:
To find the number of different forecasts containing exactly 6 correct results, we need to follow the given steps:
Step 1: Determine the total number of possible forecasts.
There are three possible outcomes for each of the 8 matches (Win, Loss or Draw). Therefore, the total number of possible forecasts is:
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3^8 = 6561
Step 2: Determine the number of ways to select 6 matches out of 8.
The number of ways to select 6 matches out of 8 is:
8C6 = 28
Step 3: Determine the number of ways to correctly predict the 6 selected matches.
For each of the 28 ways to select 6 matches out of 8, there is only one way to correctly predict the outcome of each of the 6 selected matches. Therefore, the number of ways to correctly predict the 6 selected matches is:
1 x 1 x 1 x 1 x 1 x 1 = 1
Step 4: Determine the number of ways to incorrectly predict the remaining 2 matches.
For each of the 28 ways to select 6 matches out of 8, there are 2 remaining matches that can be predicted incorrectly in 2 possible ways (Win or Loss). Therefore, the number of ways to incorrectly predict the remaining 2 matches is:
2 x 2 = 4
Step 5: Determine the total number of forecasts containing exactly 6 correct results.
The total number of forecasts containing exactly 6 correct results is:
28 x 1 x 4 = 112
Therefore, the correct answer is option C.
To find the number of different forecasts containing exactly 6 correct results, we need to follow the given steps:
Step 1: Determine the total number of possible forecasts.
There are three possible outcomes for each of the 8 matches (Win, Loss or Draw). Therefore, the total number of possible forecasts is:
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3^8 = 6561
Step 2: Determine the number of ways to select 6 matches out of 8.
The number of ways to select 6 matches out of 8 is:
8C6 = 28
Step 3: Determine the number of ways to correctly predict the 6 selected matches.
For each of the 28 ways to select 6 matches out of 8, there is only one way to correctly predict the outcome of each of the 6 selected matches. Therefore, the number of ways to correctly predict the 6 selected matches is:
1 x 1 x 1 x 1 x 1 x 1 = 1
Step 4: Determine the number of ways to incorrectly predict the remaining 2 matches.
For each of the 28 ways to select 6 matches out of 8, there are 2 remaining matches that can be predicted incorrectly in 2 possible ways (Win or Loss). Therefore, the number of ways to incorrectly predict the remaining 2 matches is:
2 x 2 = 4
Step 5: Determine the total number of forecasts containing exactly 6 correct results.
The total number of forecasts containing exactly 6 correct results is:
28 x 1 x 4 = 112
Therefore, the correct answer is option C.
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Community Answer
The results of 8 matches (Win, Loss or Draw) are to be predicted. The ...
Suppose out of the 8 matches, 6 correct results are to be predicted.
This can be done in 8C6 ways.
8C6 = 8! / 6!×2!
8C6 = 8×7×6! / 6!×2×1
8C6 = 56/2 = 28
Also, for remaining two matches result is incorrect i.e. other two possibilities.
Hence, we can select those matches 2×2=4 ways.
Total number of different forecasts containing exactly 6 correct results will be 28×4 = 112 ways.
Read more on Brainly.in - https://brainly.in/question/6448036#readmore
This can be done in 8C6 ways.
8C6 = 8! / 6!×2!
8C6 = 8×7×6! / 6!×2×1
8C6 = 56/2 = 28
Also, for remaining two matches result is incorrect i.e. other two possibilities.
Hence, we can select those matches 2×2=4 ways.
Total number of different forecasts containing exactly 6 correct results will be 28×4 = 112 ways.
Read more on Brainly.in - https://brainly.in/question/6448036#readmore
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