1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timama [110]
1 year ago
11

There are 8 tennis players in a round robin tournament, which means each team will play every other team once. How many matches

will be held during the 8-person round robin tennis tournament?​
Mathematics
1 answer:
Aliun [14]1 year ago
7 0
<h3>Answer:  28</h3>

==========================================================

Explanation:

Method 1

Imagine a table with 8 rows and 8 columns to represent all possible match-ups. You can actually draw out this table or just think of it as a thought experiment.

There are 8*8 = 64 entries in the table. Along the northwest diagonal, we have each team pair up with itself. This is of course silly and impossible. We cross off this entire diagonal so we drop to 64-8 = 56 entries.

Then notice that the lower left corner is a mirror copy of the upper right corner. A match-up like AB is the same as BA. So we must divide by 2 to get 56/2 = 28 different matches.

----------------------------------

Method 2

There are 8 selections for the first slot, and 8-1 = 7 selections for the second slot. We have 8*7 = 56 permutations and 56/2 = 28 combinations.

----------------------------------

Method 3

Use the nCr combination formula with n = 8 and r = 2

n C r = \frac{n!}{r!(n-r)!}\\\\8 C 2 = \frac{8!}{2!*(8-2)!}\\\\8 C 2 = \frac{8!}{2!*6!}\\\\8 C 2 = \frac{8*7*6!}{2!*6!}\\\\ 8 C 2 = \frac{8*7}{2!}\\\\ 8 C 2 = \frac{8*7}{2*1}\\\\ 8 C 2 = \frac{56}{2}\\\\ 8 C 2 = 28\\\\

There are 28 combinations possible. Order doesn't matter (eg: match-up AB is the same as match-up BA).

Notice how the (8*7)/2 expression is part of the steps shown above in the nCr formula.

You might be interested in
When The Product of 15 and 40 is divided by the sum of 15 and 45 what is the quotient?
BaLLatris [955]

Answer:

10

Step-by-step explanation:

(15 x 40) / (15+40)

solve inside the parenthesis:

600/60

divide:

10

6 0
3 years ago
What percent of 30 is 18
Marina CMI [18]
18 is 60 percent of 30. 3 percent is 10 percent of 30 so 3 x 6 equals 18.
4 0
2 years ago
Read 2 more answers
please help me answer these 3 questions correctly . u will get 30 pints if you do and the brainlest. please do not answer if you
stira [4]

Answer:

1

1

3

Step-by-step explanation:

6 0
2 years ago
Hi guys can u guys help me add 322 + 12
Zina [86]

Answer:

334 is the answer

Step-by-step explanation:

you add them together

4 0
2 years ago
Read 2 more answers
Peyton invested \$1700$1700 in an account that pays 3.5% interest compounded annually. Assuming no deposits or withdrawals are m
Rufina [12.5K]

Based on the amount Peyton invested, and the interest rate, the amount in the account 15 years later would be <u>$2,848.09. </u>

<h3 /><h3>How much would be in the account after 15 years?</h3>

The amount in the account after 15 years would be:

= Amount x ( 1 + rate) ^ number of years

Solving gives:

= 1,700 x ( 1 + 3.5%)¹⁵

= $2,848.09

Find out more on future value at brainly.com/question/24978019.

3 0
2 years ago
Other questions:
  • a line segment has (x1,y1) as one endpoint and (xm,ym) as its midpoint. Find the other endpoint (x2,y2)of the line segment in te
    10·2 answers
  • Find an expression equivalent to the one shown below.
    15·2 answers
  • The base of a regular pyramid is a hexagon.
    14·2 answers
  • The number of wins for a high school football team is measured for the season. When the team plays at home, it is generally beli
    14·1 answer
  • How much would 500$ invested at 9% interest compounded annually be worth after 4 years?
    13·1 answer
  • Find the equation of the line that has a slope of 14 and passes through the point (-3,12). Help me
    12·1 answer
  • Please Help.
    8·1 answer
  • Anyone know this ? I don’t understand math
    8·2 answers
  • Find the slope of the line that passes through the following points (2,5) (5,11)
    8·2 answers
  • 6(2a + b) + b A. 12a + 12b B. 12a + 7b C. 8a + 8b D. 8a – 8b
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!