Question

if k objects out of a set of n elements are placed into a fixed order, how many unique arrangements of those objects are there?

Answer 1

@amistre64 im soo lost...

Answer 2

since we cant express it as some nice little number setup, we have to define it by a formula

Answer 3

i defined the formula for it the last time ... but after each time i stated it you were still "confused"

n!/(n-k)! is the formula

Answer 4

ok.. i get that there's a formula, but i dont get how you decide which numbers to use.

Answer 5

a,b,c,d,e,f

if we take any 3 from the set and place them in a unique order; we get 60 different subsets.

5!/(5-3)! = 5*4*3 = 20*3 = 60

Answer 6

if we take k elements from a set of n elements ,,,, we can form: n!/(n-k)! unique arrangements

Answer 7

where do you get 5 from..

Answer 8

hmm, i thought i only used 5 letters :) spose we ignore the f

Answer 9

the number of elements of a set doesnt care with the elements are called; and by definition the elements that make a set are uniquly defined ... no duplicates

Answer 10

im sorry.. i am still really confused... im not just saying that so that you give me the answer, but i am homeschooled and new to this section, and i dont get the whole "!" thing or the equation and how it all works..

Answer 11

the set {a,b,c,d,e} has 5 elements

the number of ways to use 3 of those elements .....

Answer 12

! is a notation ... something that helps to shorten the way we write a number is all

Answer 13

do you recall the notation from multiple additions? say; 3+3+3+3+3+3+3 = 7(3)

do you recall the notation from multiple multiplications? say; 3*3*3*3*3*3*3 = 3^7

the notation ! expresses a different way of calculating a certain number

Answer 14

ya

Answer 15

3! is a way of expressing the number: 3*2*1 = 6

7! is a way of expressing the number: 7*6*5*4*3*2*1 = 5040

its just a notation for the way of expressing the value of the product of successive values starting at a certain number and going to 1

Answer 16

okk

Answer 17

so if it doesnt say a number, it just says a variable, how do you know what number?

Answer 18

the question tells you to use n and k .....

Answer 19

the formula for calculating the number of permutations of a set of "n" elements, by using "k" at a time amounts to: n!/(n-k)!

Answer 20

?ok.. but how do you solve it

Answer 21

by using the definition of a factorial notation ....

Answer 22

lets use the example of 5 elements ordered 3 at a time ...

what is 5! ?

Answer 23

3! is a way of expressing the number: 3*2*1 = 6

7! is a way of expressing the number: 7*6*5*4*3*2*1 = 5040

its just a notation for the way of expressing the value of the product of successive values starting at a certain number and going to 1

so what is the value of 5! ?

Answer 24

120

Answer 25

but there are no numbers with k and n

Answer 26

@amistre64

Answer 27

anyone......???