SOLUTION: What does the term "compute" mean in relation to a problem I have in which,there is the number "7" in an expontial form set to the lower front of a letter,in this case,a "C" and fo

What does the term "compute" mean in relation to a problem I have 
in which, there is the number "7" in an expontial form set to the 
lower front of a letter,in this case,a "C" and followed by the 
number "2",again in an expotinal form placed in a lower setting?

It looks somthing like example below:

               7C2
              
That means: 

"The number of combinations that can be gotten from 7 things if
you take 2 at a time"

It asks this question:

How many possible sets of 2 things each can you make from a set
of 7 things?

OR

If you have a set of 7 things, say {a,b,c,d,e,f,g}, then how many
different sets of only 2 each can you make from the set of 7?

We can make all these sets of 2:

 1. {a,b} 
 2. {a,c}
 3. {a,d}
 4. {a,e}
 5. {a,f}
 6. {a,g}
 7. {b,c}
 8. {b,d}
 9. {b,e}
10. {b,f}
11. {b,g}
12. {c,d}
13. {c,e}
14. {c,f}
15. (c,g}
16. {d,e}
17, {d,f}
18. {d,g}
19. {e,f}
20. {e,g}
21. {f,g}

So there are 21 in all. In general there are 
too many to list them all out like I did above, 
so there is a formula that gives the number 
without having to list them like the above.  It is

          n!   
nCr = ----------
       r!(n-r)!

In the case where the big set has 7 and you
want to make little sets of 2, instead of
listing them all, you just calculate:


          7!
7C2  = -------- =
       2!(7-2)!

The exclamation point means to multiply the
number before it by all positive integer
factors below it (it's called "factorial"):

 7!
---- =
2!5!


 7·6·5·4·3·2·1
---------------- =
(2·1)(5·4·3·2·1)

   
Cancel like factors in the
top and bottom

   3 1 1 1 1 1
 7·6·5·4·3·2·1
---------------- =
(2·1)(5·4·3·2·1)
 1    1 1 1 1 1


7·3 = 21

So we can get that there are 21 combinations possible
when 7 things are taken 2 at a time.

Edwin