polya's method. In how many different orders can a basketball team win exactly three out of their last five games
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Answer:
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Given: A basketball team plays 5 different matches
To find: Ways in which they can win exactly three of them
Explanation: In the five matches that are played, the results of the game can only be a win or a loss for the basketball team(since a tie is not allowed in basketball).
Since, there are exactly three wins the other two have to be losses. Therefore, we need to arrange 3 wins and 2 losses in as many ways as we can.
Let W denote winning and L denote losing.
We need to arrange W,WW,L,L .
The formula used for solving this is:
(Total games played)! / (Number of wins)! *
(Number of losses)!
= 5! / 3! 2!
= 120 / 6 *2 ( 5!= 120, 3!= 6, 2! = 2)
= 10
Therefore, there are exactly 10 ways in which a team can win exactly three out of five matches.