Permutations And Combinations Question 176

Question: A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either 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

Options:

A) $ ^{20}C _{10}\times 2^{10} $

B) $ ^{20}C _{10}\times 30^{20} $

C) $ ^{20}C _{10}\times 30^{10} $

D) $ ^{20}C _{10}\times 2^{20} $

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Answer:

Correct Answer: A

Solution:

  • [a] Matches whose prediction 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} $