Find both the number of combinations and the number of permutations for the given number of objects.

15 objects taken 7 at a time​

Answers

Answer 1

Answer:

First, if we have a set of K elements, such that are ordered as:

{x₁, x₂, ...}

The total number of permutations for the K elements can be found in the next way.

For the first element in the set, we have K options.

For the second element in the set, we have (K - 1) options (because we already choose one)

For the third element we have (K - 2) options, and so on.

The total number of permutation is equal to the product between the numbers of options for each position's element, then the number of permutations for K elements is:

permutations = K*(K - 1)*(K - 2)*....*2*1 = K!

Now suppose that we have a set of N elements, and we want to make groups of K elements.

The total number of different combinations of K elements is given by the equation:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case we have 15 objects (then  N = 15) and we take 7 at the time (Then K = 7)

Where we need to take in account the number of combinations and also the permutations for each combination.

Then the total number of different sets is:

C(15*7)*7!

First, the total number of combinations will be:

[tex]C(15,7) = \frac{15!}{(15 - 7)!7!} = \frac{15!}{8!*7!} = \frac{15*14*13*12*11*10*9}{7*6*5*4*3*2*1} = 6,435[/tex]

So we have 6,436 combinations, and each one of these combinations has 7! permutations.

permutations = 7! = 7*6*5*4*3*2*1 = 5,040

if we combine these we get:

Combinations*Permutations = 6,435*5,040 = 32,432,400

Answer 2

Answer:

7

Step-by-step explanation:


Related Questions

What percent of the model is shaded green?

Answers

Answer:

1/5%

Step-by-step explanation:

The percentage of the model shaded green will be 20.

How to find how much percent 'a' is of 'b'?

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

The total number of the box in the figure is 100.

The total number of shaded green = 20

So,

[tex]\dfrac{20}{100} \times 100[/tex]

20%

Therefore, The percentage of the model shaded green will be 20.

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Lee la siguiente información.
En una olimpiada matemática, cada estudiante recibe un punto por cada pregunta acertada que tenga, en la siguiente tabla de frecuencias se muestra la clasificación de la cantidad de estudiantes de acuerdo con su puntaje obtenido.



De acuerdo con la tabla, ¿cuál es aproximadamente la desviación estándar?
A.
6,12
B.
7
C.
8,42
D.
9

Answers

La desviación estándar se puede calcular mediante la fórmula

S = √∑fx² / n - (∑fx / n) ²

La desviación estándar es 6,12

Poner los valores de la tabla en la hoja de Excel dada.

s = √381430 / 60 - (4770/60) ²

s = √6357.167 -6320.25

s = √36,917

s = 6,0759

Cuando se redondea daría 6,1

The standard deviation can be calculated using the formula

S= √∑fx²/n - (∑fx/n)²

The standard deviation is 6.12

Putting the values from the table in the given excel sheet.

s= √381430/60 - (4770/60)²

s= √6357.167 -6320.25

s= √36.917

s= 6.0759

When rounded would give 6.1

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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

I'd say D

Step-by-step explanation:

Find the 70th term of the arithmetic sequence 29, 17, 5

Answers

Answer:

857

Step-by-step explanation:

70th term = a + d(n-1)

d= 29-17=12

a=29

n-1 = 69

70th term = 29 + 12×69

= 29 + 828

= 857

The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges 1 for the first time they service your lawn, and the price will multiply by a factor of 0.90 every week thereafter. Green Thumbs charges 400 for the first time they service your lawn, and then charges an additional 45 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?

Answers

Do you need help or u just wanted the answer

help me with this please ​

Answers

Answer:

A

Step-by-step explanation:

Brainliest PLEASE

Write an equation to represent the following description. Seventeen more than eight times a number is −6.

Answers

8x + 17 = -6


(you can use a different variable to replace x if you need to :D)

help me pls mathhh mhm

Answers

Answer:

f = -15

Step-by-step explanation:

3(f/3) equals f

3(-5) equals -15

The final equation becomes: f = -15

Solve for x.



O 72.5
O 31.6
O 26
O 11.9

Answers

answer 11.9


D aka))h)

sorry if its twisted but i need help in # 3 please :)

Answers

Answer:

knsy standard ka question hy

Step-by-step explanation:

(4-3i)(1+2i)
I have so many of these

Answers

Answer:

-6i^2+5i+4

Step-by-step explanation:

Rearrange Terms

(-3i+4)(1+2i)

(-3i+4)(2i+1)

Distribute

-3(2i+1)+4(2i+1)

-6i^2-3i+4(2i+1)

-6i^2-3i+4(2i+1)

-6i^2-3i+8i+4

Combine Liker Terms

-6i^2+5i+4

Solution

-6i^2+5i+4

Answer:

-2 + 5i

Step-by-step explanation:

Remember these rules:  

real times real = real (e. g., 4(1) = 4)

real times imaginary:  imaginary (e. g., 4(2i) = 8i)

imaginary times real imaginary

imaginary times imaginary:  real with a negative sign (e. g., (-3i)(2i) = +6

          Once again:  work out (-3i)(2i).  We get (i^2)(-6) = +6

In summary:  your (4-3i)(1+2i) becomes 4 + 8i - 3i - (i^2)(-6), or

                                                                 4 + 5i - 6, or   -2 + 5i

Solve for x and round to the nearest tenth.
х
54
22

Answers

Answer:87 hope

this helps

Step-by-step explanation:

PLZ IT'S VERY IMPORTANT
Find the perimeter​

Answers

Answer:

118 cm

Step-by-step explanation:

8 + 16 + 22 + 29 + (29-16) + (8+22) = 118 cm

64x = 8.
What is the value of x that makes the equation true?
Enter the correct answer in the boxes.
2

Answers

Answer:

x = 1/8

Step-by-step explanation:

The value of x is 1/8.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

64x = 8

Solve for x.

64x = 8

Divide both sides with 64.

x = 8/64

x = 1/8

Thus,

The value of x is 1/8.

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is 8 a solution to 1/2x+9=13?

Answers

Answer:

yes

Step-by-step explanation:

 solve for x by simplifying both sides of the equation, then isolating the variable.

x = 8

x = -3.
3.2 2 - 16=(x-1)=?

Answers

Answer:

dvide it

Step-by-step explanation:

All I'm asking is help me and don't rip me off I'm being generous

Answers

Answer:

the eqaution would be

C=1.25h-0.5

The solution for 4 boxes would be

4.50 dollars

Step-by-step explanation:

Well c in this case is total

h is the amount of boxes

Since each box (h) cost $1.25 each, you multiply 1.25 by h.

Then that one time coupon off his total would be just -0.50

Hi I just need the sum for this :) (Sum is the answer)
4(2x + 3) ÷ 5y = ?

Answers

Answer:

23

Step-by-step explanation:

I need help will mark brainlist

When solving -1/8 (x + 35) = - 7, what is the correct sequence of the operations?

1. multiply each side by -1/8, add 35 to each side

2. multiply each side by -1/8, subtract 35 from each side

3. multiply each side by -8, subtract 35 from each side

4. multiply each side by -8, add 35 to each side​

Answers

Answer:

The correct option is 3.

Step-by-step explanation:

By multiplying each side by -8, you can get rid of the fraction. Then by subtracting 35 from both sides, you get what is x.

Pls help 10 ptsssssssssssss
NO LINKS

Answers

4.5. 4x4.5=18. 18 divided by 4 is 4.5

solve this equation -3x - 8 = 18

Answers

8.67 (rounded to the nearest tenth)

Solve for the value of a.
(8a)•\(5a-2)
Answer: a =
Submit Answer
о
attempt 1 out o

Answers

Answer:

a = 14

Step-by-step explanation:

The angles share a common side terminal side, so they are supplementary angles. This also means they add up to 180º.

8a + (5a - 2) = 180

Combine like terms.

13a - 2 = 180

13a = 182

Divide both sides by 13.

a = 14

This is your answer.

Check your work by plugging "a" back into the original equation.

8a + (5a - 2) = 180

8(14) + [5(14) - 2] = 180

112 + (70 - 2) = 180

112 + 68 = 180

180 = 180

Your answer is correct.

Hope this helps!

what is the value of v in 2.5v = 125

Answers

Answer: v=50

Step-by-step explanation:

 2.5 v=125

v=125/2.5

v=50

Answer:

v=50

Step-by-step explanation:

[tex]\frac{2.5v}{2.5} =\frac{125}{2.5}[/tex]    divide both sides by 2.5 to isolate v

v=50

Please help I’ll mark you as brainliest if correct

Answers

Answer:

The answer you clicked is correct.

Step-by-step explanation:

1 teacher = 25 scholars.

I need help with this now

Answers

Answer:

80

hope this is correct

comment below

hope this helps you ☺️☺️

For the rectangle shown, which equation can be used to find the value of x?​

Answers

Answer:

Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex]

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\x^{2} +3.6^{2} =7.4^{2} \\x^{2} +12.96=54.76\\x^{2} =\sqrt{41.8} \\x=6.47\\[/tex]

The value of x is 6.46 inch.

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Given: breadth = 3.6, diagonal= 7.4

Using Pythagoras theorem,

H²=P²+B²

(7.4)²= (3.6)²+B²

54.76=12.96 + B²

54.76-12.96=B²

41.8= B²

B= 6.46 inch.

Hence, the value of x is 6.46 inch.

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hi can anyone help me with this

Answers

Answer:

i think you should multiply 6cm by 8 cm by 10 cm ..sorry if it was not vlear but i try:)

I need help on the pcture​

Answers

Answer:

Where is it?

Step-by-step explanation:

You need to add a picture

Ceasar opens a bank account and makes an initial deposit of $800. The banker tells Ceasar that he is going to receive an annual rate of 10% compounded continuously on his investment. Find the bank balance assuming Ceasar leaves the account untouched for 8 years.


Can you please do the problem using the formula A(t)=pe^(rt).

Answers

Answer:

1780.43

Step-by-step explanation:

Given:

P = 800

r = 10% or 0.1

t = 8

1780.43 i just took the test jit

A bottled water distributor wants to determine whether the mean amount of water contained inâ 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water is 0.008 gallon. You select a random sample of 50 bottles, and the mean amount of water perâ 1-gallon bottle is 0.995 gallon.

Required:
a. Is there evidence that the mean amount is different from 1.0 gallon?
b. What is the test statistic?
c. Compute theâ p-value and interpret its meaning.
d. Construct a 95% confidence interval estimate of the population mean amount of water perâ 1-gallon bottle.

Answers

Answer:

1. There is evidence that mean is different from 1.0 gallon

2. test statistic = -4.42

3. p value = 0.00001

4. 0.9928,0.9972

Step-by-step explanation:

h0: u = 1.0

h1: u not equal to 1.0

alpha = 0.05

sd = 0.008

n = 50

mean = 0.995

standard error se = 0.008/√50 = 0.00113

test statistics calculation

0.995-1/0.00113

= -0.005/0.00113

= -4.42

p value calculation

using the z test statistics and alpha = 0.05

the p value using a p value calculator = 0.00001

0.00001<0.05

so we Reject the null hypothesis

we conclude there is enough evidence that mean is different from 1.0

95% confidence interval

Z alpha/2 = 0.025

we find z value using excel function

NORMSINV (0.025)

|Z| = 1.96

Standard error se = 0.00113

margin of error E = 1.96 x 0.00113 = 0.0022148

confidence interval =

0.995 - 0.0022148, 0.995 + 0.0022148

= 0.9928, 0.9972

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