# App that counts probabilities in c++

1. Jan 8, 2014

### Hepic

Hey,I am making an app that counts probabilities in c++(win32){for those who knows}.
I have found three formulas of equation,but I need some help for one.

For example we have a die,and we hit it 6 times.
Can we count with an formula,the probabilities to have the number "5",three times exactly?(no less,no more)

Thanks!!!

2. Jan 8, 2014

### mathman

Use the binomial theorem.
k out of n with probability p of success on one roll (q=1-p), is pkq(n-k)n!/{k!(n-k)!}.
Your example: n = 6, k = 3, p = 1/6.

3. Jan 9, 2014

### Hepic

Can you explain more because I hear about that first time?

Or you could send me a tutorial??

4. Jan 9, 2014

5. Jan 9, 2014

### Hepic

Yea,I found an intersting site called "Math is fun",and I undestood it,but how I can count probabilities with that?

6. Jan 9, 2014

### Staff: Mentor

For the example in your original post:

You cast the die six times, so there are $6^6$ equally likely sequences of results. Because they are equally likely, the probability of getting any given sequence is one in $6^6$. How many of these sequences include exactly three fives?