Team a and team b play each other in a best out of 7 tournament. so the team that wins 4 games first wins the tournament. how many possible sequences are there for team a to win? examples: , aaaba, aabaa, etc.

There are 35 ways.

Step-by-step explanation:

Consider the provided information.

In order to find the number of possible sequences we have few case:

Case I: If team A will win all 4 games without losing any match.

A A A A

There is only 1 way as you can see, Because after winning 4 games in a row no need to play again.

Case II: If team A will win 4 games out of 5 games.

A A A B A, or A A B A A, or A B A A A, or B A A A A,

Remember A A A A B  this is not going to include.

That means there are 4 possible ways if team B win one match.

Case III: If team A will win 4 games out of 6 games.

It means team A needs to win 3 games from first 5 games so that after wining 6th match they win the tournament.

So the number of ways are

That means there are 10 possible ways if team B win two match.

Case IV: If team A will win 4 games out of 7 games.

It means team A needs to win 3 games from first 6 games so that after wining 7th match they win the tournament.

So the number of ways are

That means there are 20 possible ways if team B win three match.

Thus, the total number of ways are: 1 + 4 + 10 + 20 = 35

Hence, there are 35 ways.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

b i think

step-by-step explanation:

not really sure