Permutation, Mathematics

Assignment Help:

Permutation

- It is an order arrangement of items whether the order must be strictly observed

Illustration

Assume x, y and z be any of three items. Arrange these in all possible permutations NB: The above 6 permutations are the maximum one can ever acquire in a situation whereas there are only 3 items however if the number of items exceeds 3 then determining the number of permutations by outlining as done above may be cumbersome. Thus we use a special formula to find out such permutations. The formula is specified below

The number of permutations of 'r' items taken from a sample of 'n' items may be given as nPr =(n!)/((n - r)! )

whereas; ! = factorial

For illustration

i. 3P3 =(3!)/((3 - 3)! )

= (3 * 2 * 1) / )0!               Note that  0! = 1

6/1 = 1

ii. 5P3 = (5!)/((5 - 3)! )

= (5 * 4 *3 * 2 * 1) / )1 * 2

= 60

iii. 7P5 =          (7!)/((7 - 5)! )

= (7 * 6 *5 * 4 *3 * 2 * 1) / )1 * 2

= 5040/2

= 2520

SYSTEMS OF ODE, Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2  2 linear s...

Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2  2 linear systems of ODE. (1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems are topologi

Derivatives, What are the ingredients of a Mathematical Model? What is a mo...

What are the ingredients of a Mathematical Model? What is a model?

Exponential and logarithm equations, Exponential and Logarithm Equations ...

Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol

PROBABILITY.., Urn A contains 1 white,2 black and 3 red balls;Urn B contain...

Urn A contains 1 white,2 black and 3 red balls;Urn B contains 2 white,1 black and 1 red balls;and Urn C contains 4 white,5 black and 3 red balls.One urn is chosen at random and two

Operations, i dont now how to do it

i dont now how to do it

Calculate maximum area of the triangle, if the sum of lengths of hypotenuse...

if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3

Perfimeter and area, all perimeter and area

all perimeter and area

Fractions rates and ratios, In 6th grade I am learning about ratios rates a...

In 6th grade I am learning about ratios rates and fractions. I am working on vmathlive.com and need serious.

Equations, 20 equations that equal 36

20 equations that equal 36

Calculate how much ribbon is needed to wrap the box, Ribbon is wrapped arou...

Ribbon is wrapped around a rectangular box that is 10 by 8 by 4 in. Using the example provided, calculate how much ribbon is needed to wrap the box. consider the amount of ribbon d  