Question

QuizBIGPOINT

Answer 1

The number of permutations of the problem is

1. This = 24
2. Outfit = 360

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Combination

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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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The Formula :

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$\frac {n!}{k! (n-k)!}$

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Permutation

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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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The Formula :

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$\frac {n!}{k!}$ (With Double Elements)

n! (Without Double Elements)

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Factorial

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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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For example

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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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The Formula :

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n! (Combined Multiplication)

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Place Filling Rules

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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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The formula

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n1 × n2 × n3 × ... × nr

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Question

Find the number of permutations of letters of the word

- this

- outfit

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Answer

"Number One"

=》This = Four Letters ( 4! )

P = 4!

P = 1 × 2 × 3 × 4

P = 2 × 3 × 4

P = 6 × 4

P = 24

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"Number Two"

=》Outfit = Six Letters ( 6! )

=》Outfit = Two Letters The Same ( "T" ) = 2!

P = $\frac {1×2×3×4×5×6}{2×1}$

P = $\frac {2×3×4×5×6}{2}$

P = $\frac {6×4×5×6}{2}$

P = $\frac {24×5×6}{2}$

P = $\frac {120×6}{2}$

P = $\frac {720}{2}$

P = 360

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Conclusion

So, the number of permutations of the problem is

1. This = 24
2. Outfit = 360

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Learn More

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1. ➽ brainly.com/question/24659851
2. ➽ brainly.com/question/14767366
3. ➽ brainly.com/question/1216161

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Answer Detail

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• ➽ Subject: Mathematics
• ➽ Class : 12
• ➽ Chapter : 7 - The Rule of Counting:
• ➽ Maple Code
• ➽ Categorization code : 12.2.7
• ➽ Keywords : This, Outfit