Quandaries and Queries
  

 

I have a math question i am stumped on for one of my classes. The question states that there are 14 baseball games with 2 possible outcomes for each game, visitor win or home win. How many different total combinations are possible from the 14 games?

could you please show me how to do it mathematically for any number of games...with the same 2 outcomes, visitor or home win...thanks.

Paavn

there are 12 games with two possible outcomes for each game, can you please tell me how to calculate all the possible outcomes. For example, 12 baseball games, with either visitor or home outcome, how can i figure out all the possible baseball game combinations?

Laddi
 

 

Hi,

Imagine that you are going to create a list of all possible outcomes. Each outcome will be a string of H's and V's, H means the home team won and V means the visiting team won. For example

HHVH...

means the home team won games 1 and 2, the visiting team won game 3, the home team won game 4,...

After the first game there are only two possible lists

  1. H
  2. V

For the second game, each of these could be extended in two ways, either by adding an H or a V. Thus after game 2 there are 4 possible lists

  1. HH
  2. HV
  3. VH
  4. VV

For the third game, each of these could be extended in two ways, either by adding an H or a V. Thus after game 3 there are 8 possible lists

  1. HHH
  2. HHV
  3. HVH
  4. HVV
  5. VHH
  6. VHV
  7. VVH
  8. VVV

I hope you see now what is happening. After each game the number of possible lists is double what you had after the previous game. That is

  • Game 1: 2 lists
  • Game 2: 2 2 = 22 = 4 lists
  • Game 3: 2 2 2 = 23 = 8 lists
  • Game 4: 2 2 2 2 = 24 = 16 lists

Penny

  
 

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