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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?
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The results of 8 matches (Win, Loss or Draw) are to be predicted. The ...
Solution:

This is a problem of combination.

Total number of possible outcomes for 8 matches = 3^8 (each match can have 3 possible outcomes)

= 6561

Number of ways of getting exactly 6 correct results out of 8 matches:

Choose 6 matches out of 8 matches in = 8C6 ways

For each of these 6 matches, there is only one correct outcome.

For the remaining 2 matches, there are 2 possible outcomes.

Number of ways of choosing 2 matches out of 2 remaining matches = 2C2 = 1

Total number of ways of getting exactly 6 correct results out of 8 matches = 8C6 * 2^2 = 112

Therefore, the correct answer is (c) 112.
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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?
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