a school sent 5 students to a spelling bee.the team was made up of 4 people. how many different teams of 4?

Question

students could be sent

Answer 1

That's called a combination problem.
http://mathforum.org/dr.math/faq/faq.comb.perm.html

It uses "!" read factorial, which is the product of the number times each smaller integer. So 5! = 5 X 4 X 3 X 2 X1

Here's the formula:

5!
--
4!(5-4)!

You can ignore the 1's and cancel out factors to divide easily.

5 X 4 X 3 X 2 X1
-----------------------
4 X 3 X 2 X 1 X 1

= 5.

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Answer 2

5 different teams (out of the 5 students) could make up a different 4 person team.

Answer 3

5 teams can be chosen

If the students are A,B,C,D,E
In each situation only one student can be left home:

A,B,C,D (E left home)
A,B,C,E (D left home)
A,B,D,E (C left home)
A,C,D,E (B left home)
B,C,D,E (A left home)

For the official Math this is called 5 choose 4.
The Formula would be 5!/[1!(5-1)!]
where 5! means 5*4*3*2*1 or 5*4!
5!/[1!(5-1)!]=(5*4!)/(1!4!)
Since 4! is on top and bottom it crosses out.
5/1! (well 1!=1) so 5/1=5

Answer 4

5 ....

because there would be 20 people and 20/4 is 5