Question

how many ways can a music teacher arrange 24 students in 3 rows?

Answer 1

First I guess you must have 8 students in each row right?

Answer 2

yes that would be correct..

Answer 3

And do you know how to calculate the number of ways 8 people can be arranged in a row?

Answer 4

use a calculator?

Answer 5

Well you will need a calculator to do it

Have you heard of factorial 8. :- 8!

Answer 6

8! = 8*7*6*5*4*3*2*1

Answer 7

And as there is also 3 rows the calculations is

3! * 8!

Answer 8

thanks!!!

Answer 9

Yw

Answer 10

In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 20 students

Answer 11

would that be 5!*4!

Answer 12

@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.

Answer 13

Or, alternatively, you can write this as \((3!)^8\dbinom{24}3\dbinom{21}3\cdots\dbinom63\).

Answer 14

This assuming order matters, which by the context I think we can assume it does.