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alex41 [277]
3 years ago
9

How long does it take to become an orthodontist?

Mathematics
1 answer:
Marat540 [252]3 years ago
7 0
Https://www.careervillage.org/questions/9768/how-many-years-does-it-take-to-become-an-orthodontist

I hope this helps you. :)
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What is Permutations and Combinations?
marissa [1.9K]

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.

5 0
2 years ago
Difference of squares examples
bazaltina [42]
Triangle, rectangles, pollygon, robtuse, i hope this is what you mean

8 0
3 years ago
Help me please I’ll mark brainliest thank you
jenyasd209 [6]

Answer:

11/15=x/240

240/15=16

11 x 16=176

11/15=176/240 or rather he completes 176 passes

Step-by-step explanation:

4 0
3 years ago
Which expression has the same value as 12 − 6 ÷ 3
Juli2301 [7.4K]
Answer is a.
Due to BIDMAS/BODMAS
anything that is first, in this case division, goes into brackets.
6 divided by 3 would go into brackets making you solve that first then u would subtract your answer by 12 making your answer 4

Answer is a.

a.
5 0
1 year ago
Read 2 more answers
Pls follow the steps on the image
Darina [25.2K]

Answer:

-4

Step-by-step explanation:

7 0
3 years ago
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