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
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.

You might be interested in
If m<1 is 115 what is m<4​
aniked [119]

I'm not sure if this is right, but I multiplied 115 by 4 and got 460- Try that? ;^;

4 0
3 years ago
Find the equation of the line.<br> Use exact numbers.
kvasek [131]

Answer:

y=-3/2x+3

Good luck:)

5 0
3 years ago
This doctor has the right to assist this patient because
alexandr402 [8]

Answer:

She is licensed by the government to practice medicine

Step-by-step explanation: When a Medical Doctor has completed his studies and have been lincensed to practice, this lincense confer certain rights to the Medical Doctor. One of the rights given to Medical Doctors is the right to assist a patient by providing curative treatment or preventive treatments and other requirements by the patient. Prior to obtaining a lincense a Medical Doctor must pass through certain exams regulated by Government.

3 0
3 years ago
The width of a rectangle measures (9h 1) centimeters, and its length measures
Yanka [14]

Answer:

(22h - 8) centimeters

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

= 2{(9h - 1) + (2h - 4)}

= 2(9h - 1 + 2h - 4)

= 2(11h - 4)

= (22h - 8) centimeters

5 0
3 years ago
An expression is given. 3 × (8 + 2) ÷ 2 Which statement is true about the parentheses in this expression?
muminat

Answer:

I don't think you typed the full problem, but the answer is either that you do the parenthesis first, or that it adds to 10

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • What two dimensional cross sections can we create by slicing a cube
    6·1 answer
  • Rewrite the following parametric equations in rectangular form.<br><br> x=e^3t<br> y=e^-t
    10·1 answer
  • HELP PLEASE!!!!!!!!!!!
    13·1 answer
  • To inscribe a hexagon inside a circle, to which length should you set your compass in order to draw the six vertices?
    13·1 answer
  • Help Please. Need answer immediately
    6·2 answers
  • 15 points for this question
    10·1 answer
  • Can u pls help me with this question ​
    12·1 answer
  • Mr. Schmidt cuts 1/4 of a piece of construction paper. He uses 1/5 of the piece to make a flower. What fraction of the sheet of
    14·1 answer
  • Whats the slope for 3x + 2y = -10
    14·2 answers
  • Find value ill post the other stuff after u answer this​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!