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Llana [10]
2 years ago
9

What is Permutations and Combinations?

Mathematics
1 answer:
marissa [1.9K]2 years ago
5 0

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

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PQ

SR

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Step-by-step explanation:

they are all going down while the others rise

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3/4x - 6y = 18<br>what's the x intercepts and y intercepts?​
mash [69]

Answer:

X: (24,0)

Y(0,-3)

Step-by-step explanation:

X-intercept:

.75x-6y=18

plug in 0 for y

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(24,0)

Y-intercept:

plug in 0 for x

.75(0)-6y=18

divide by -6

y=-3

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7 0
3 years ago
A retailer allowed 12% discount and sold a T-shirt at a loss of Rs 16. If he had sold it at 10% discount he would have gained Rs
Murrr4er [49]

Answer: Marked Prixe = Rs. 1800

Step-by-step explanation:

Let the marked price be M

1) A retailer allowed 12% discount and sold a T-shirt at a loss of Rs 16.

SP = 0.88M

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CP = 16 + SP

CP = 16 + 0.88M

2) If he had sold it at 10% discount he would have gained Rs 20.

SP = 0.9M

SP - CP = 20

0.9M = 20 + CP

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36 = 0.02M

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3 years ago
The function h(x) = 12x8 + 49 is an even function. Which transformation of h(x) would result in a function that is neither even
Irina-Kira [14]

Answer:  translation 8 units to the right

Step-by-step explanation:

An even function is a function such that:

h(x) = h(-x)

and the function is odd if:

h(-x) = -h(x)

Now, let's talk about transformations:

A) Reflection over the x-axis:

When we have a point (x,y) and we do a reflection over the x-axis, the reflected point will be:

(x, -y).

Then for the case of a function:

y = h(x).

then the reflection will be:

g(x) = - y = -h(x).

And if h(x) is even, -h(x) is also even, so this is not the correct option.

B) Vertical stretch by a factor of 7.

This is written as:

g(x) = 7*h(x).

then:

g(x) = 7*h(x)

g(-x) = 7*h(-x) = 7*h(x) = g(x)

the transformation is even.

C) Translation of 8 units to the right.

We can write this as:

g(x) = h(x - 8).

Then:

g(-x) = h(-x -8) = h(x + 8)

Then g(-x) is not equal to g(x)

and also g(-x) ≠ -g(x)

So in this case the transformation is neither odd or even.

C)  horizontal compression by a factor of One-half.

This transformation is written as:

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And, similar as the case of the vertical compression, in this case the transformation is also even.

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Pani-rosa [81]

Answer:

D

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Here, we want to select which of the options explains the scenario in the question.

Firstly, 1,000 shares were purchased at $10 per share.

Mathematically the total amount of shares bought will be 10 * 1000 = $10,000

Also, we have the growth rate as 12.5% = 12.5/100 = 0.125

Thus, representing the scenario with a function, we have;

A(t) = 10,000 e0.125t

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3 years ago
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