The number of permutations of the problem is
- This = 24
- Outfit = 360
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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.
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
(With Double Elements)
n! (Without Double Elements)
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.
- 》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
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.
6! x2! - 3! : 4!
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.
n! (Combined Multiplication)
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.
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
"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 =
P =
P =
P =
P =
P =
P = 360
So, the number of permutations of the problem is
- This = 24
- Outfit = 360
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<h2>Learn More</h2>- ➽ Subject: Mathematics
- ➽ Class : 12
- ➽ Chapter : 7 - The Rule of Counting:
- ➽ Maple Code
- ➽ Categorization code : 12.2.7
- ➽ Keywords : This, Outfit
