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. The total number of ways in which he can make the predictions such that exactly 10 predictions are correct, are equal to

Step-by-step solution

In order to predict exactly 10 correct predictions, ⇒ we have to select 10 matches out of 20 in 20 C 10 ways ⇒ ways of making a correct prediction for each match is 1 , so for 10 matches it is equal to 1 10 = 1 . ⇒ Remaining 10 predictions must be wrong so for each incorrect prediction we have 2 choices out of 3 , this can be done in 2 10 ways. Hence, the required number of ways = 20 C 10 1 ⋅ 2 10 = 20 C 10 × 2 10 .