A person predicts the outcomes of $20$ cricket matches of his home team. Each match can result in a either 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

^{20} C_{10} \times 2^{10}

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^{20} C_{10} \times 3^{20}

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^{20} C_{10} \times 3^{10}

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^{20} C_{10} \times 2^{20}

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Solution

The correct option is A $^{20} C_{10} \times 2^{10}$
Matches whose predictions are correct can be selected in $^{20} C_{10}$ ways. Now each wrong prediction can be made in $2$ ways. Thus, the total number of ways is $^{20} C_{10} \times 2^{10}$ .

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A person predicts the outcomes of 20 cricket matches of his home team. Each match can result in a either 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

The correct option is A 20C10×210Matches whose predictions are correct can be selected in 20C10 ways. Now each wrong prediction can be made in 2 ways. Thus, the total number of ways is 20C10×210.

A person predicts the outcomes of $20$ cricket matches of his home team. Each match can result in a either 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

The correct option is A $^{20} C_{10} \times 2^{10}$
Matches whose predictions are correct can be selected in $^{20} C_{10}$ ways. Now each wrong prediction can be made in $2$ ways. Thus, the total number of ways is $^{20} C_{10} \times 2^{10}$ .