Solving for A Variable in Combination

[lacrotix]

Homework Statement

Solve for $$_5C_n$$ = 10

The Attempt at a Solution

$$_5C_n$$ = 10

$$\frac{5!}{n!(5-n)!}=10$$

$$\frac{120}{n!(5-n)!}=10$$

I can't go on from there. I remember that my teacher told me that for combinations and permutations, if the variable is the second number (or number to the right of the big letter), that you have to try to simply the best you can logically, and then guess based on hunches. I also remember him also saying that looking at the equation will help you make an "informed hunch."

The problem is, I don't think I simplified my problem right to make these guesses. I guess I can always guess and check straight from the beginning, but I think there should be an easier way than brute force guessing and checking. Especially if the equation is something like:

$$_2_5_0C_n = 2573000$$

Any ideas?

Also, is there an easier way of typing in math equations for homework help. It is so difficult for me to guess with the Online LaTeX Equation Editor. Yuck!

 

[eumyang]

$$\frac{120}{n!(5-n)!}=10$$

I don't see any way besides guess-and-check at the moment. It's pretty obvious that
$$n!(5-n)!=12$$
and assuming that
$$0 \le n \le 5$$
there won't be many guesses you'll have to make until you find your answer. (BTW, there are two answers.)

Also, is there an easier way of typing in math equations for homework help. It is so difficult for me to guess with the Online LaTeX Equation Editor. Yuck!

You can find guides easily enough that show how to type equations in LaTeX. Just keep practicing and it won't be difficult after a while.

 

[lacrotix]

Thanks eumyang.

That description and logic-checking helps a whole lot.