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
LenaWriter [7]
3 years ago
6

7. Eleven students go to lunch. There are two circular tables in the dining hall, one can seat 7 people, the other can hold 4. I

n how many ways can they be seated
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
7 0

Answer:

239,580 ways of seating

Step-by-step explanation:

11 students will be divided into 2 groups. One group of 7 people and one group of 4 people. So first we need to find the number of ways of dividing 11 students into these 2 groups.

First group is of 7 people. We have to select 7 people out of 11. The order of selection does not matter so this is a combination problem. Selecting 7 people from 11 can be expressed as 11C7.

Formula for combination is:

^{n}C_{r}=\frac{n!}{r!(n-r)!}

For the given case this would be:

^{11}C_{7}=\frac{11!}{7! \times 4!}=330

So, there are 330 ways of selecting a group of 7 from 11 students. When these 7 students are selected the remaining 4 will go to the other group. So, we can say there are 330 ways to divide the 11 students in groups of 7 and 4. Note that if you start with group of 4 students, the answer will still the same because 11C4 is also equal to 330.

Next we have to arrange 7 students on a round table. The number of possible arrangements would be = (7 - 1)! = 6! = 720

Similarly, to arrange 4 people on a round table, the number of possible arrangements would be = (4 - 1)! = 3! = 6

Since, for each selection of the 330 groups, there are 720 + 6 possible seating arrangements, so the total number of possible seating arrangements would be:

330 ( 720 + 6) = 239,580 ways

Thus, there are 239,580 ways of seating 11 students.

You might be interested in
Paco orders an ice cream for $1, but realizes his wallet is at home and he only has 3/20 of $1 with him. If his mom pays the rem
Svet_ta [14]

Answer: the answer is c) $0.85


Step-by-step explanation:

if he has 3/20 of a dollar that calculates to $0.15 and $1.00 minus $0.15 equals $0.85

3 0
3 years ago
Question Progress 10 Homework Progress 17/ x: y = 2:3 Which is the correct equation? A 2x = 3y B 2y = 3x C y = x - 1 D y = x + 1
gtnhenbr [62]

Answer:  2y = 3x

Reason:

The equation x:y = 2:3 is the same as saying x/y = 2/3

Cross multiply to get 3x = 2y which flips to 2y = 3x

3 0
1 year ago
HELP PLEASE ,, i need the right answer
____ [38]

Answer:

It's the first one

4 0
3 years ago
Read 2 more answers
Find the value of X (in this picture)​
alexgriva [62]

Answer:

x = 89

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

x+32+ 59 = 180

Combine like terms

x + 91 = 180

Subtract 91 from each side

x +91-91= 180-91

x = 89

6 0
3 years ago
13 divided by $85.02
Salsk061 [2.6K]
The answer is 0.15290519877
6 0
3 years ago
Read 2 more answers
Other questions:
  • HELPPPP HURRYYYYYYY A bag contains 150 marbles which are red, green, and blue. Suppose a student randomly selects a marble witho
    9·1 answer
  • What is a common factor of 14, 6, 9
    9·2 answers
  • Two angles are vertical angles. One angle is 2x the other angle is labeled (x+30). Find the value of x
    12·1 answer
  • What is the slope of the line containing (–2, 5) and (4, –4)?
    14·2 answers
  • Whats 25% of 90 in full explanation
    12·2 answers
  • 3 4 8 11 44 49 What is the next number?
    13·1 answer
  • The shorter leg of a right triangle is 9 ft shorter than the longer leg. The hypotenuse is 9 ft longer than the long leg. Find t
    5·1 answer
  • 6(x + 5) = 3(x - 14) ?
    8·2 answers
  • URGENT NEED HELP. What is the approximate length of AB?
    12·2 answers
  • Will be marked the brainliest if correct
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!