anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@amistre64 im soo lost...
amistre64
  • amistre64
since we cant express it as some nice little number setup, we have to define it by a formula
amistre64
  • amistre64
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

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anonymous
  • anonymous
ok.. i get that there's a formula, but i dont get how you decide which numbers to use.
amistre64
  • amistre64
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
amistre64
  • amistre64
if we take k elements from a set of n elements ,,,, we can form: n!/(n-k)! unique arrangements
anonymous
  • anonymous
where do you get 5 from..
amistre64
  • amistre64
hmm, i thought i only used 5 letters :) spose we ignore the f
amistre64
  • amistre64
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
anonymous
  • anonymous
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..
amistre64
  • amistre64
the set {a,b,c,d,e} has 5 elements the number of ways to use 3 of those elements .....
amistre64
  • amistre64
! is a notation ... something that helps to shorten the way we write a number is all
amistre64
  • amistre64
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
anonymous
  • anonymous
ya
amistre64
  • amistre64
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
anonymous
  • anonymous
okk
anonymous
  • anonymous
so if it doesnt say a number, it just says a variable, how do you know what number?
amistre64
  • amistre64
the question tells you to use n and k .....
amistre64
  • amistre64
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)!
anonymous
  • anonymous
?ok.. but how do you solve it
amistre64
  • amistre64
by using the definition of a factorial notation ....
amistre64
  • amistre64
lets use the example of 5 elements ordered 3 at a time ... what is 5! ?
amistre64
  • amistre64
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! ?
anonymous
  • anonymous
120
anonymous
  • anonymous
but there are no numbers with k and n
anonymous
  • anonymous
@amistre64
anonymous
  • anonymous
anyone......???

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