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What is arrangement in physics?
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How many ways are there when clockwise and anti-clockwise arrangements are the same?
Arranging Objects. The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1. Example. How many different ways can the letters P, Q, R, S be arranged? The answer is 4! = 24. This is because there are four spaces to be filled: _, _, _, _
- Reminder - Factorial Notation
- Theorem 2 - Number of Permutations
- Theorem 3 - Permutations of Different Kinds of Objects
- Theorem 4 - Arranging Objects in A Circle
- Exercises
Recall from the Factorial section that n factorial (written n!\\displaystyle{n}!n!) is defined as: Each of the theorems in this section use factorial notation.
The number of permutations of n distinct objects taken r at a time, denoted by Prn\\displaystyle{{P}_{{r}}^{{n}}}Prn, where repetitions are not allowed, is given by
The number of different permutations of n objects of which n1 are of one kind, n2 are of a second kind, ... nk are of a k-th kind is
There are (n−1)!\\displaystyle{\\left({n}-{1}\\right)}!(n−1)! ways to arrange ndistinct objects in a circle (where the clockwise and anti-clockwise arrangements are regarded as distinct.)
Exercise 1
In how many ways can 6\\displaystyle{6}6 girls and 2\\displaystyle{2}2boys be arranged in a row (a) without restriction? (b) such that the 2\\displaystyle{2}2boys are together? (c) such that the 2\\displaystyle{2}2boys are not together? Answer
Exercise 2
How many numbers greater than 1000\\displaystyle{1000}1000 can be formed with the digits 3,4,6,8,9\\displaystyle{3},{4},{6},{8},{9}3,4,6,8,9if a digit cannot occur more than once in a number? Answer
Exercise 3
How many different ways can 3\\displaystyle{3}3 red, 4\\displaystyle{4}4 yellow and 2\\displaystyle{2}2 blue bulbs be arranged in a string of Christmas tree lights with 9\\displaystyle{9}9sockets? Answer
Combinations. There are also two types of combinations (remember the order does not matter now):. Repetition is Allowed: such as coins in your pocket (5,5,5,10,10); No Repetition: such as lottery numbers (2,14,15,27,30,33)
A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A= {1,6} is 2, such as {1,6}, {6,1}. As you can see, there are no other ways to arrange the elements of set A.
- What is permutation?Permutation is a way of changing or arranging the elements or objects in a linear order.
- What is the formula for permutation?The formula for permutation for n objects taken r at a time is given by: P(n,r) = n!/(n-r)!
- What are the types of permutation?The permutation of an arrangement of objects or elements in order, depends on three conditions: When repetition of elements is not allowed When r...
- What is the formula for permutation when repetition is allowed?Let n be the number of objects and r be the selection of objects, then if repetition is allowed, the permutation of objects will be n × n × n × ……(...
- What is the permutation for multisets?The permutation formula for multisets where all the elements are not distinct is given by: n!/(P1!P2!…Pn!)
5 days ago · A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The number of permutations on a set of n elements is given by n!
5 days ago · The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation (order is significant). The division of space into cells by a collection of hyperplanes (Agarwal and Sharir 2000) is also called an arrangement.
2 days ago · In combinatorics, a permutation is an ordering of a list of objects. For example, arranging four people in a line is equivalent to finding permutations of four objects. More abstractly, each of the following is a permutation of the letters a, b, c, a,b,c, and d d: \begin {aligned} → \ & a, b, c, d\\ → \ & a, c, d, b\\ → \ & b, d, a, c ...
