Two chess players, A and B, are going to play 7 games. Each game has three possibleoutcomes: a win for A (which is a loss for B)
1 answer:
Answer:
A) the possible outcomes for individual game is 210 games.
B) The possible outcome for this is 357 games.
C) Then the Possible Games are 267 games.
Step-by-step explanation:
A) Total number of individual games are 7 in which A ends up with 3 wins which give 4 remaining games. then there are two draw games from them. and in the end the remaining games are losses so,we useformula for combination:
B) Now Player A has 4 point that gives us 5 possibilities until we reach 7 games. Similarly B have 3 points which is same as player A gives us 5 possibilities until we reach 7 games. thus those two cases for player A and Player B can be stated as:
C) Lets say that player A ahs 4 points and player B has 3 points and all seven games have been played so.
c1) If player A has 4 wins and 3 losses then last win have to be in 7th match thus:the answer is .
c2) If player A has 3 win, 2 draws and 3 losses thus it means that final match cannot be a loss thus the answer is .
c3) Now lastly if player A has 1 win and 5 draws we can arrange them arbitrarily thus the answer here is .
c4) now If player A has 2 wins, 4 draws and 2 losses thus answer is
Sum of all the cases is
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