Students are given a list of ten vocabulary words to learn. In how many ways could four of the words be listed on a test?
Is this permutation or combination??

Question

Students are given a list of ten vocabulary words to learn. In how many ways could four of the words be listed on a test?
Is this permutation or combination??

anonymous · Answer

@mathmale

mathmale · Answer

It'd be worth looking up "permutation" and "combination" to get a better idea of what each means.

I'd call the present situation a "combination:"  the number of ways in which we could choose from 10 distinct objects 4 at a time.

Here, n = 10 (n is the number of distinct objects we have from which to choose)
         x = 4 (the number of objects taken at any one time)

                                      C 
We want to evaluate  10     4.

Have you any previous experience in evaluating combinations such as this?

mathmale · Answer

$$_{10}C _{4}=\frac{ 10! }{ 4!(10-4)! }$$

mathmale · Answer

Note:  n!   means "n factorial," and is equal to n(n-1)(n-2)(n-3)....1.
So:  4! = 4*3*2*1=24

anonymous · Answer

thanks so much! I knew how to do both combinations and permutations I just could not figure out which this one was to do it!