NFT -Need math help
 

Since it seems to be homework day on CP, I was hoping there were some math wizzes around. In the past, there were a few math majors around, IIRC.

My wife is helping out with the Math Is Cool team at our middle school and has run into a problem that she can't explain how to do mathematically. I am no help here because I sucked at probability in college.

The problem goes something like:"Cindy is buying four balloons. She can pick from any of four different colors. How many unique combinations can she make?"

On first thought, it would just be 4x4x4x4 (256). However, some of those combinations are duplicates (RRBB = RBBR). You can brute force it out by listing the different combinations to get the answer of 35 but this is too slow for a competition.

Any help on how to explain this mathematically so the kids can do the problem quickly? :shrug:

4x3x2x1=

The solution is this. Cindy is way to high maintenance to be involved with. She needs to decide on one freakin balloon color to make it easier. If she needs different ones, then get all 4 colors. Cindy probably asks for 3 different salad dressings all on the side too. She probably needs to have the lights off to have sex as well. Tell ya what. Keep away from this chick.

Nope, because you can repeat colors.

The answer is 35, but I'm just not sure how to get it.

Are they filled with heroin?

It makes a difference.

My wife is a math geek. If you don't have an answer for this by the time she gets home I'll have her take a look at it.

Here's the equation you want:

(n+r-1)!
-----------
r! * (n-1)!

In your case,

n (number from which to choose) = 4
r (number chosen) = 4

So the equation reduces to this:

7!
-------
4! * 3!


or

7*6*5 * 4!
-----------
4! * 3!

which is 35.

well...

never mind then :)

For sure not a math genius here, but wouldn't it be 4 to the 4th like your first thought?

(4+4-1)! / (4! * 3!) = 7! / 144 = 5040/144 = 35

Damn it.. beat me to it!

Wow....you guys are smart.

I had a flashback to factorials as i was thinking about it, but i wasn't sure how it applied to this situation.

Thanks, TipRoast!

Beat me to it. Always get this confused with permutations and combinations.

Me too. I went through a lot of high end math to get my engineering degree but I always had a brain lock on this stuff.