Question
A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :
- 20C10.210
- 20C10.210
- 20C10.310
- 20C10.220
Hint:
Total number of ways in which he can make the predictions so that exactly 10 predictions are correct =
The correct answer is: 20C10.210
Matches whose prediction are correct can be selected in 
ways.
Since each match can result either in a win, loss or tie for the home team.
Now, each wrong prediction can be made in two ways (i.e. the correct result is win and the person predicts either lose or tie)
and there are 10 matches for which he predicted wrong.
Total number of ways in which he can make the predictions so that exactly 10 predictions are correct =
Thus, total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to
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