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Natasha_Volkova [10]
3 years ago
10

Give the difinition, formula, and example problem of permutation, combination & probability... please asap huhu I'll mark yo

u as the brainliest if can do this ​
Mathematics
2 answers:
SSSSS [86.1K]3 years ago
7 0

Answer:

Answer:

Permutation:

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Formula:

nPr=\frac{n!}{(n-r)!}

Example:

Permutations are the different ways in which a collection of items can be arranged. For example, the different ways in which the alphabets A, B and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different.

Combination:

In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.

Formula:

nCr=\frac{n!}{r!(n-r)!}

Example:

Combination: Picking a team of 3 people from a group of 10.

C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Formula:

Conditional Probability P(A | B) = P(A∩B) / P(B)

Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)

Example:

Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and its being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.

Mariulka [41]3 years ago
5 0

<em><u>~permutation~</u></em>

Permutation is a term that in mathematics refers to several different meanings in different areas.

Permutation can be permutation with repetition and permutation without repetition.

nPr=

(n−r)!

n!

<em><u>~</u></em><em><u>Permutation</u><u> </u><u>without</u><u> </u><u>repetition</u></em><em><u>~</u></em>

Permutation means to combine the default elements in all possible ways so that each group contains all the default elements.

The number of permutations of a set of n different elements is equal Pn=n×(n-1)×...×2×1=n!

<em><u>~</u><u>Permutation with repetition</u><u>~</u></em>

If between n given elements there are k1 equals of one kind, k2 equals of another kind,..., ky equals of rth kind, we speak of permutations with repetition.

<em><u>~combinations without repetition~</u></em>

In many counting problems, the order of the selected elements is not important.

Each choice of r different elements of an n-member set determines one of its subsets that has r elements, we call it a combination of r-th class without repetition of n elements.

nCr=

r!(n−r)!

n!

<em><u>~combinations with repetition~</u></em>

Repetition combinations are combinations in which elements can be repeated.

<em><u>~Variations without repetition~</u></em>

A variation of the r-th class in an n-membered set is each ordered r-torque of different elements.

(We can determine this number using the principle of consecutive counting).

<em><u>~Variations with repetition~</u></em>

If the elements in ordered r-tuples can be repeated we are talking about variations with repetition.

(We can determine this number using the principle of consecutive counting).

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N+3(n-1)<br> n plus three ( n minus 1
liq [111]

Answer:

3n^2+-3

Step-by-step explanation:

nxn +nx(-1) +3xn+ 3x(-1)

3 0
3 years ago
Consider <img src="https://tex.z-dn.net/?f=%24%5Ctriangle%20ABC%24%20such%20that%20%24BC%20%3D%203AC%24%20and%20%24%5Cangle%20A%
Gemiola [76]

The answer to the question is,

12 sin(∠B) = 2,           12 sin(∠C) = √3+√35

Sin rule is,

sin(A)/BC = sin(B)/AC = sin(C)/AB

sin(B) = (sin(A)×AC)/BC

sin(C) =(sin(B)×AB)/AC

To solve this question we apply sin rule,

Now we take

12 sin(∠B) =12 (sin(∠A)×AC)/BC

12 sin(∠B) =12 (sin(π/6)×(x/3x))          where ∠A =π/6 and AC=x, BC =3x

12 sin(∠B) =12 ((1/2)×(1/3))

12 sin(∠B) =12/6 = 2

12 sin(∠B) = 2

now we find the value of 12 sin(∠C)

12 sin(∠C) = 12(sin B)×(AB/BC)

now put the value of 12 sin(∠B) = 2

12 sin(∠C) = 2×(AB/BC)

12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]

12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]

cos (π/6) = √3/2 and BC/AC =3

then

12 sin(∠C) = 2×[(√3/2)+3×(cos B)]

cos B= √1-sin²B

12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]

12 sin(∠B) = 2

sin B = 1/6

12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]

12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]

12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]

12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]

12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]

12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]

12 sin(∠C) = 2×[(1/2)(√3+√35)]

12 sin(∠C) = √3+√35

Hence the answer is,

12 sin(∠B) = 2,         12 sin(∠C) = √3+√35

Learn more about triangles rules from:

brainly.com/question/27998693

#SPJ10

6 0
2 years ago
State the x- and y-intercepts.
Rufina [12.5K]

1. Y-Intercepts are where the graph crosses the y-axis. For a parabola, this occurs once, at (0, -3) in the graph shown.

2. X-Intercepts are where the graph crosses the x-axis. For a parabola, this occurs twice, at (-1, 0) and (3, 0) in the graph shown.

3. A parabola that is positive opens upwards, while a parabola that is negative opens downwards. Therefore, this parabola is positive.

Hope this helps!! :)

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In the diagram shown, XYZ is a dilation<br> of TUV. The center of the dilation is<br> point W.
saw5 [17]

There ain't no diagram here, DAWGG :/

6 0
3 years ago
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Q5 Q2.) Find a positive angle less than 360degrees that is coterminal with the given angle.
SCORPION-xisa [38]
Coterminal angle<span> is an </span>angle which has <span>the same initial and terminal side of the original angle. It can be found by adding or subtracting 360deg.

A positive angle less than 360 that is coterminal with -85 is = -85 + 360
= 275 degree</span>
7 0
3 years ago
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