Pickleball is a game played by two people. The first player to score 18 points w

Question

Pickleball is a game played by two people. The first player to score 18 points wins, provided that player is at least 2 points ahead. Otherwise, play continues until one player gets 2 points ahead, at which time he is declared the winner. However, the first player to reach a score of 24 wins the game even if he is not 2 points ahead.

Mike and Harvey are playing Pickleball and they wonder how many possible outcomes there could be. Here are some possible final scores:

Mike wins 18 to 0
Mike wins 18 to 1
Mike wins 18 to 2
Harvey wins 23 to 21
Harvey wins 24 to 22
Harvey wins 24 to 23

This is only a partial list of possible outcomes. How many outcomes would be in the list if ALL possible outcomes were listed?

Explanation / Answer

Their are two set of outcome

First the outcomes can be

18 - 0

18-1

...

...

18-16

and say Mike wins.

So their are (16+1)=17 possible choices.

Now since any one can win this choices are valid for both of them so 2*17 = 34 choices

At the second case where the situation is

18-17

their lies a possibility of the following choices

24-17,24-18, ...24-23(altogether 7 choices) and Mike wins

OR

if the first stage yields with 18-18

then thhe cases are

24-18-,24-19,...24-23 (altogether 6 choices ) and Mike wins.

So total no. choices are 6+7=13 ways

Now since we have chosen arbitrarily one the actual no. of ways is 2*13 =26

So there will be altogether 34+26 = 60 kinds of final result can appear.

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