The number of permutations of the problem is
- This = 24
- Outfit = 360
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<h2>Combination</h2>
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Combinations are the number of ways to choose members from a certain number, namely from members of a set, combinations can also be interpreted as many ways to make subsets, namely with a certain number of members, namely from members of a set, if a set has n members then the selection of r members, and the combination of n is where r is less than n.
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<h3>The Formula : </h3>
![\:](https://tex.z-dn.net/?f=%5C%3A)
<h2>
![\frac {n!}{k! (n-k)!}](https://tex.z-dn.net/?f=%5Cfrac%20%7Bn%21%7D%7Bk%21%20%28n-k%29%21%7D)
</h2>
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<h2>Permutation</h2>
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Permutations are a way to determine the number of arrangements that occur by paying attention to the order. So in permutations, position/order is very important, namely AB is considered different from BA (AB ≠ BA). Permutation formula
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<h3>The Formula :</h3>
![\:](https://tex.z-dn.net/?f=%5C%3A)
(With Double Elements)
n! (Without Double Elements)
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<h2>Factorial</h2>
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The factorial of a natural number is the successive multiplication of a natural number that begins with the number one and arrives at the natural number, the factorial is used in calculating combinations, probabilities, and permutations.
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<h3>For example</h3>
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- 》2! = 1 × 2
- 》3! = 1 x 2 x 3
- 》4! = 1 x 2 x 3 x 4
- 》5! = 1 x 2 x 3 x 4 x 5
- 》6! = 1 × 2 × 3 × 4 × 5 × 6
- 》7! = 1 × 2 × 3 × 4 × 5 × 6 × 7
- 》8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8
- 》9! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
- 》10! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10
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The following is an example of a factorial that does not involve mixed arithmetic operations, so if you want to add it up we just need to calculate it like a normal number, a factorial number that only multiplies the difference between a factorial number that is added up by addition, subtraction, multiplication, division, for example see below.
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6! x2! - 3! : 4!
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The example above is a mixed arithmetic operation that contains multiplication, subtraction, and division. Remember that in mixed arithmetic operations, multiplication/division must be completed before addition/subtraction.
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<h3>The Formula : </h3>
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n! (Combined Multiplication)
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<h2>Place Filling Rules</h2>
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The Place Fill Rule is a method or method that can be used to determine the number of ways an object occupies its place. The filling slots rule is a method of calculating how many possible ways there are in an experiment or event. If a first event can be done in m different ways and the second event can be done in a different way and so on until the last event in k.
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<h3>The formula</h3>
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n1 × n2 × n3 × ... × nr
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<h2><u>Question</u></h2>
Find the number of permutations of letters of the word
- this
- outfit
![\:](https://tex.z-dn.net/?f=%5C%3A)
<h2><u>Answer</u></h2>
"Number One"
=》This = Four Letters ( 4! )
P = 4!
P = 1 × 2 × 3 × 4
P = 2 × 3 × 4
P = 6 × 4
P = 24
==========
"Number Two"
=》Outfit = Six Letters ( 6! )
=》Outfit = Two Letters The Same ( "T" ) = 2!
P = ![\frac {1×2×3×4×5×6}{2×1}](https://tex.z-dn.net/?f=%5Cfrac%20%7B1%C3%972%C3%973%C3%974%C3%975%C3%976%7D%7B2%C3%971%7D)
P = ![\frac {2×3×4×5×6}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B2%C3%973%C3%974%C3%975%C3%976%7D%7B2%7D)
P = ![\frac {6×4×5×6}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B6%C3%974%C3%975%C3%976%7D%7B2%7D)
P = ![\frac {24×5×6}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B24%C3%975%C3%976%7D%7B2%7D)
P = ![\frac {120×6}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B120%C3%976%7D%7B2%7D)
P = ![\frac {720}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B720%7D%7B2%7D)
P = 360
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<h2><u>Conclusion</u></h2>
So, the number of permutations of the problem is
- This = 24
- Outfit = 360
![\:](https://tex.z-dn.net/?f=%5C%3A)
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<h2>Learn More</h2>
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- ➽ brainly.com/question/24659851
- ➽ brainly.com/question/14767366
- ➽ brainly.com/question/1216161
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<h2>Answer Detail</h2>
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- ➽ Subject: Mathematics
- ➽ Class : 12
- ➽ Chapter : 7 - The Rule of Counting:
- ➽ Maple Code
- ➽ Categorization code : 12.2.7
- ➽ Keywords : This, Outfit