anonymous
  • anonymous
how many ways can a music teacher arrange 24 students in 3 rows?
Algebra
schrodinger
  • schrodinger
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welshfella
  • welshfella
First I guess you must have 8 students in each row right?
anonymous
  • anonymous
yes that would be correct..
welshfella
  • welshfella
And do you know how to calculate the number of ways 8 people can be arranged in a row?

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anonymous
  • anonymous
use a calculator?
welshfella
  • welshfella
Well you will need a calculator to do it Have you heard of factorial 8. :- 8!
welshfella
  • welshfella
8! = 8*7*6*5*4*3*2*1
welshfella
  • welshfella
And as there is also 3 rows the calculations is 3! * 8!
anonymous
  • anonymous
thanks!!!
welshfella
  • welshfella
Yw
anonymous
  • anonymous
In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 20 students
anonymous
  • anonymous
would that be 5!*4!
anonymous
  • anonymous
@welshfella I think there's more to the first problem, but I could be wrong. We're not explicitly told whether the same 8 people are seated in any given row. I think this means we have \(8!\dbinom{24}8\) (or \({}_{24}P_8\)) ways of seating the first 8 students in one row, then \(8!\dbinom{16}8\) in the next, and finally \(8!\dbinom88\) in the third. So in my mind there may be as many as \((8!)^3\dbinom{24}8\dbinom{16}8\) ways of seating 24 students in 3 rows.
anonymous
  • anonymous
Or, alternatively, you can write this as \((3!)^8\dbinom{24}3\dbinom{21}3\cdots\dbinom63\).
anonymous
  • anonymous
This assuming order matters, which by the context I think we can assume it does.

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