Question

Give students are to present projects to the class. One of the students asked to go first. Allowing for this request, in how many ways can the students be ordered for making their presentation. (I have the answer. I just don't know how they got it.)

Answer 1

This is a permutation problem.
Let's say you have n number of students total. Then, the general equation would be:
\[n! = n \times (n-1) \times (n - 2) \times ... \times 1\]
In this case, however, it would look more like:
\[(n-1)! = (n - 1) \times (n - 2) \times ... \times 1\]
How many students are there in total?

Answer 2

5

Answer 3

So the answer should be:
\[(5-1)! = 4! = 4 \times 3 \times 2 \times 1 = 24\]

Answer 4

You rock. Thanks! Can I ask one more? What are the factors of 5m^4p^3-5m^2p^5

Answer 5

Sure, if the equation is:
\[5m^4 \times p^3 - 5m^2 \times p^5\]
They are:
\[5 m^2 \times (m + p) \times (m - p) \times p^3\]

Answer 6

How did you get the (m+p) part?

Answer 7

First, factor out 5m^2 from both sides:
\[5m^2(m^2 \times p^3 - p^5)\]
Factor out p^3 from both sides:
\[5m^2 \times p^3 \times (m^2 - p^2)\]
The last part of the equation can be factored as follows:
\[(m^2 - p^2) = (m +p)(m-p)\]
Substituting in gives the result I gave in my last answer.

Answer 8

Thanks a tom!

Answer 9

Tom

Answer 10

Stupid supporters. Ton

Answer 11

Autocorrect ergggg