Suppose we want to choose 5 colors, without replacement, from 18 distinct colors.
(a) If the order of the choices does not matter, how many ways can this be done?
(b) If the order of the choices matters, how many ways can this be done?
Answers
Considering the definition of permutation and combination:
the number of ways of choosing 5 colors from 18 distinct colors (the order doesn't matter) is 8,568.the number of ways of choosing 5 colors from 18 distinct colors (the order of choices matters) is 1,028,160.Definition of PermutationPermutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
take all the elements of a set.the elements of the set are not repeated.order matters.To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
Definition of combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following formula is applied:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
This caseIn this case, you know we want to choose 5 colors, without replacement, from 18 distinct colors. This is:
We want to choose 4 colors: n= 5The total number of distinct colors: m= 18(a) If the order of the choices is not taken into consideration, you use a combination as follow:
[tex]C=\frac{18!}{5!(18-5)!}[/tex]
Solving:
[tex]C=\frac{18!}{5!13!}[/tex]
C= 8,568
Finally, the number of ways of choosing 5 colors from 18 distinct colors (the order doesn't matter) is 8,568.
(b) If the order of the choices matters, you use a permutation as follow:
[tex]18P5=\frac{18!}{(18-5)!}[/tex]
Solving:
[tex]18P5=\frac{18!}{13!}[/tex]
18P5= 1,028,160
Finally, the number of ways of choosing 5 colors from 18 distinct colors (the order of choices matters) is 1,028,160.
Learn more about
permutation:
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combination:
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Max's solar pool cover is 10 feet wide by 32 feet long. If it had a 1.5 ft overhang,
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Answers
(1) 2x + 3y = 31 y
(2) 2x + 3y = x + 7
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(3) x = 31y - 7
(2) 2(31y - 7) + 3y = 31y - 7 + 7 ; 62y - 14 + 3y = 31y ; 34y = 14 ; y = 14/34 ; y = 7/17
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Answers
Answer:
Variance: 26.5
Standard Deviation: 5.1478150704935
Step-by-step explanation:
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Answer:
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Answers
Answer:
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I'm not sure what you mean but I'll provide both.
5/8 + 3/4
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The wavelength measurement of the figure is,
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The figure is shown in image.
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Which of the following expressions represents 3 less than 5 times a number
A) 5n - 3
B) 5 - 35
C) 3n - 5
D) 3 - 5
Answers
Answer:
A)
Step-by-step explanation:
The correct expression which represents ''3 less than 5 times a number'' would be,
A) 5n - 3
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that,
A mathematical expression is,
''3 less than 5 times a number''
Let us assume that,
A number = x
Hence, the expression to represent ''3 less than 5 times a number'' is,
⇒ (5 × n) - 3
⇒ 5n - 3
So, the correct option is,
A) 5n - 3
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What is the equation of the line that passes through the point (-5,0) and has a
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This should be your answer
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The perimeter of a semicircle is 5.14 inches what is the semicircle radius
Answers
Answer:
Radius = 1 in.
Step-by-step explanation:
Let the radius be 'r'. Diameter = 2r
Perimeter of a semicircle = Circumference of semi circle + Diameter
[tex]=>\pi r + 2r = 5.14 in.[/tex] (Let the value of π be 3.14)
[tex]=> 3.14r + 2r = 5.14in.\\=>5.14r=5.14\\=>r =\frac{5.14}{5.14} =1in.[/tex]
Help i don’t know if my answers are correct and I need the other ones I didn’t answer to be answered to please help I need the correct answer for 1-8 I need to bring my grade up
Answers
1) correct
2) correct
3) Not Congruent
4) Not Congruent
5) correct
6) Not Congruent
7) incorrect
8) SAS
Explanation:
7 is incorrect because the angle isn’t included in the sides
Hope this helps!
HELP PLS FOR BRAINLIEST
The square of m reduced by 32.
2m - 32
m^2 - 32
32 - m^2
m^2 + 32
The product of 5 and r, and then increased by k.
5r - k
5r + k
k - 5r
5r/k
A number x is tripled and then decreased by 10.
3x - 10
3x + 10
x^3 - 10
x^3 + 10
8 reduced by the sum of x and y.
8(x - y)
(x + y) - 8
8 - (x + y)
8 + (x + y )
4 more than the product of 8 and n.
8n - 4
8n + 4
4(8 + n)
(8 + n) - 4
6 less than the sum of 9 and d.
6 - 9d
9d + 6
6 - (9 + d)
(9 + d) - 6
Eighty less than four times a number.
4x - 80
4x + 80
4x / 80
80 - 4x
Yvonne (y) runs three times as fast as Xavier (x). What is an algebraic translation of this?
y = 2x
y = 3x
y = 1/2x
y = 1/3x
n divided by 5
n/5
5n
n + 5
n - 5
a take away 19
a - 19
19 - a
a + 19
19a
Answers
Answer:
The square of m reduced by 32
m^2 - 32
The product of 5 and r, and then increased by k
5r + k
A number x in tripled and then decreased by 10
3x - 10
8 reduced by the sum of x and y
8 - (x + y)
4 more than the product of 8 and n
8n + 4
6 less than the sum of 9 and d
(9 + d) - 6
Eighty less than four times a number
4x - 80
Yvonne (y) runs three times as fast as Xavier (x). What is an algebraic translation of this?
y = 3x
n divided by 5
n/5
a takeaway 19
a - 19
Every month, Veronica deposits $230 in an account with an interest rate of 6% compounded monthly. How much money will she have in the account at the end of the first 5 years? (Round to the nearest cent. Do not enter the $ sign.)
Answers
Answer:
Veronica will have $310.04 at the end of first five years.
Step-by-step explanation:
Principal Amount P = $230
Interest Rate r = 6%
Time t = 5 years
Compounded monthly n = 12
We need to find the future amount (A)
The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and finding A
[tex]A=P(1+\frac{r}{n})^{nt}\\A=230(1+\frac{0.06}{12})^{5*12}\\A=230(1+0.005)^{60}\\A=230(1.005)^{60}\\A=230(1.348)\\A=310.04[/tex]
So, Veronica will have $310.04 at the end of first five years.
If connie pays $100 for 8 baskets, what is the unit rate for each Basket?
Answers
The unit rate is $12.50 per basket
is the relationship in this picture a function
if so why?
Answers
Answer:
PLEASE BE CAREFUL NightmareMech14 IS A PREDATOR HE ASKS FOR VIDEOS OF GIRLS AND TRYS TO GET THEM TO EMAIL HIM DONT GIVE HIM ANY INFORMATION STAY SAFE COPY AND PASTE THIS EVERYWHERE
Step-by-step explanation: