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
ANTONII [103]
3 years ago
15

There are 5 lead male roles and 4 lead female roles. If you must seat the male leads together, the female leads together, the 3

producers together, and the director by himself, how many different ways can you seat the 13 people around the circular table?
Mathematics
2 answers:
LuckyWell [14K]3 years ago
5 0

Answer with explanation:

Number of Male lead roles = 5

Number of female lead roles =4

Number of Producers =3

There is a single director.

Total number of people who will sit around circular table

=5+4+3+1

  =13

The answer can be explained in the following way.Suppose there are three people A,B and C who have to sit around a circular table.

When it has to be arranged in linear way it can be arranged in 3! ways which are: A B C,A CB, B AC,B C A,C A B,C BA.

When these are arranged in circular arrangement,ABC , B CA,CAB are same.

So,in a linear arrangement each six of the arrangement of ABC is different and there are three different Circular arrangement of ABC.

So, total number of Circular Arrangement

                     =\frac{3!}{3}\\\\=2

As,3!=3 ×2×1

→→So, total number of arrangement of 13 different person when they are seated around a circular table such that  male leads together, the female leads together, the 3 producers together, and the director by himself

=There are four things that is 5 male, 4 female,3 Producer and 1 Director considering male as 1, female as 2, Producer as third and director as 4,there are 4 things which need to be arranged in a circular table

       \rightarrow \frac{4!\times 5! \times 4! \times 3! \times 1!}{4}\\\\=\frac{24 \times 120 \times 24 \times 6}{4}\\\\=24 \times 120 \times 6 \times 6\\\\=103680    

→n!=n×(n-1)×(n-2)×(n-3).........1            

tiny-mole [99]3 years ago
4 0

Answer:

24, 414,720 or 5,391,360 depending on the level of precision you (or your teacher) want. :-)

Step-by-step explanation:

The best way to approach this problem is to do it in two phases.  First, consider the groups (and the top level permutations), then you consider the individuals (within the groups).  There's even a third level to consider, the starting position around the table.

Before going into the solution, let's do a little warm-up using the producers group of 3.  Since we talk about arranging the 13 people at the table (and not just the groups), the order of the individuals within a group is also important.  Just looking at the producers, how many ways can we sit them (among themselves)?  6 ways: {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a}

That is governed by the following formula, since we are taking ALL the possible elements (unlike a lottery draw for example): P(n) = n!

This solution, we'll need the following grouping possibilities:

P(1) = 1, P(3) = 6, P(4) = 24 and P(5)=120

Real solution starts here

First level

First, we have to see how many arrangements are possible based on the groups...how many ways can we sit the actors, the actresses, the producers and the director as groups?  There are 4 groups to consider, so the result for the groups arrangements is P(4) = 24 ways.

Second level

Now, for each of those 24 ways to arrange the groups, so they are sat together around the table) we also have to take into account the internal arrangements within each group... because as we've seen, there are 6 ways to sit the producers.

So, for the producers, we have P(3) = 6 as we've seen

For the actresses, we have P(4) = 24

For the actors, we have P(5) = 120

For the director group, we have P(1) = 1

So, for each of the 24 ways to arrange the sequence of groups, we also have 17,280 (6 * 24 * 120 * 1) ways to arrange people within the groups.

That makes a total of 24 * 17,280 = 414 720 ways to arrange the people around the table.... not taking into account the seat number.

Third level

If you want to take into account the fact that one of the 414 720 arrangements is different if the first person sits on the chair #1 than if it sits on chair #2 and so on... then we have to multiply these 414 720 arrangements by 13 to represent the various possible starting point for the arrangement.  For a grand total of 5 391 360

So, the answer is your choice, 24, 414,720 or 5,391,360 depending on the level of precision you (or your teacher) want. :-)

You might be interested in
HELP I NEED THIS ANSWERED!!!!!!! MY MOM WILL KILL ME​
Damm [24]

Answer: i think it's 16

8 0
3 years ago
MARK AS BRAINLIEST
labwork [276]

Answer:

C [-2 < x]

Step-by-step explanation:

-6(x - 2) < 24

________ ___

-6 -6

x - 2 > -4

+ 2 + 2

_________

x > -2

** Whenever you divide\multiply by a negative, you reverse the inequality symbol.

I am joyous to assist you anytime.

6 0
3 years ago
How to solve using substitution<br> y=3/4X+5<br> 4x-3y=-1
Pachacha [2.7K]
Please, use parentheses to enclose each fraction:
y=3/4X+5 should be written as <span>y=(3/4)X+5

Let's eliminate the fraction 3/4 by multiplying the above equation through by 4:

4[y] = 4[(3/4)x + 5]
Then 4y = 3x + 20
(no fraction here)

Let 's now solve the system   

4y=3x + 20
4x-3y=-1

We are to solve this system using subtraction.  To accomplish this, multiply the first equation by 3 and the second equation by 4.  Here's what happens:

12y = 9x + 60  (first equation)
16x-12y = -4, or -12y = -4 - 16x (second equation)

Then we have 

 12y = 9x + 60
-12y =-16x - 4

If we add here, 12y-12y becomes zero and we then have 0 = -7x + 56.
Solving this for x:  7x = 56; x=8

We were given equations   
</span><span>y=3/4X+5
4x-3y=-1

We can subst. x=8 into either of these eqn's to find y.  Let's try the first one:

y = (3/4)(8)+5 = 6+5=11

Then x=8 and y=11.

You should check this result.  Subst. x=8 and y=11 into the second given equation.  Is this equation now true?</span>
5 0
3 years ago
The ratio of boys to girls at a movie is . If there are 21​ girls, how many boys are at the​ movie?
Aliun [14]
Id there are 21 girls according to my calculations there would be a heap amount of boys which is 23
7 0
2 years ago
When you convert 100 ft per second to inches per second, will there be more or less than 100 inches.Explain
Serga [27]

There are 12 inches in a feet, so there are 1200 inches. 1200 inches is more than 100 inches, so there is more.


6 0
3 years ago
Other questions:
  • Find the slope of a line perpendicular to the line whose equation is 4y + 5x = 16.
    10·1 answer
  • Frank finished 65% of his math homework before dinner. If this amount represents 26 problems,How many problems will Frank need t
    14·1 answer
  • A snail moves 1/50 a mile in 5/6 of an hour. If the snail continues at this pace, how far, in miles, does it move in one hour?
    10·1 answer
  • PLZ HELP IM BEGGING YOU. Just answer 12 and 13
    10·1 answer
  • It's possible to build two triangles with all the same angles that are not comgruent
    7·1 answer
  • 15 X 10^5 in scientific notation
    7·1 answer
  • Is -1 1/2 rational?
    9·2 answers
  • If u risk a dollar to flip a coin heads 4 times in a row and are paid only 12 dollars if u win, how much are you being shortchan
    12·1 answer
  • Marcos sees a cake advertised as $15 or 2 for $25. What is the difference of the unit rate?
    10·1 answer
  • Can someone please help me with solving this maths question?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!