# Probability of 6 heads if flipping 10 coins 10 times

I am learning probability on my own (I am not taking any class). I came across this question while learning the the binomial probability distribution formula.

How do I use the binomial distribution formula to solve the following question? What is the probability of getting six heads when flipping 10 coins 10 times.

Does it affect thing that 10 coins are flipped 10 times or 100 times?

I messed it up with the question: What is the probability of 6 heads if flipping 2 coins 5 times. Then n will be 10...

• stats.stackexchange.com/tags/self-study/info Commented Feb 1, 2017 at 16:51
• I'm voting to close this question as off-topic because this is a very elementary question. Commented Feb 1, 2017 at 17:28
• @MichaelChernick, Is it against site rules to ask elementary questions? Does that make something off topic? :-o Commented Feb 1, 2017 at 17:56
• Elementary questions are likely to have been answered many times in possible duplicates. Commented Feb 1, 2017 at 18:28
• Thank you for adding the [self-study] tag. Please read its wiki. You need to tell us what you understand thus far, what you've tried (other than that you've searched the internet for the answer) & where you're stuck. We'll provide hints to help you get unstuck. Commented Feb 1, 2017 at 18:58

If the probability of heads if $p$, the six heads happen with probability $p^6$ and the four tails with probability $(1-p)^4$. There are 10 possible places for the 6 heads, so you need to multiply by the number of ways that can happen: ${10 \choose 6} = 210$, so the answer is
$${10 \choose 6} p^6 (1-p)^4$$
If the coin is fair, this equals $210 \times (0.5)^{10} \approx 0.20$